Proceedings of the American Mathematical Society最新文献

英文中文

Automorphism groups of affine varieties consisting of algebraic elements 代数元素组成的仿射变体的自形群

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16759

Alexander Perepechko, Andriy Regeta

Given an affine algebraic variety <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper X"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding="application/x-tex">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove that if the neutral component <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal upper A normal u normal t Superscript ring Baseline left-parenthesis upper X right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant="normal">A</mml:mi> <mml:mi mathvariant="normal">u</mml:mi> <mml:mi mathvariant="normal">t</mml:mi> </mml:mrow> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">mathrm {Aut}^circ (X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the automorphism group consists of algebraic elements, then it is nested, i.e., is a direct limit of algebraic subgroups. This improves our earlier result (see Perepechko and Regeta [Transform. Groups 28 (2023), pp. 401–412]). To prove it, we obtain the following fact. If a connected ind-group <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper G"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding="application/x-tex">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> contains a closed connected nested ind-subgroup <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H subset-of upper G"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>⊂</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">Hsubset G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and for any <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g element-of upper G"> <mml:semantics> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">gin G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> some positive power of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="g"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding="application/x-tex">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> belongs to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.

给定仿射代数簇 X X，我们证明如果自变群的中性分量 A u t ∘ ( X ) mathrm {Aut}^circ (X) 由代数元组成，那么它是嵌套的，即是代数子群的直接极限。这改进了我们之前的结果（见 Perepechko 和 Regeta [Transform. Groups 28 (2023), pp.）为了证明这一点，我们得到以下事实。如果一个连通的吲哚群 G 包含一个封闭的连通嵌套吲哚子群 H ⊂ G Hsubset G ，并且对于任意 g ∈ G gin G，g 的某个正幂次属于 H H ，那么 G = H G=H 。

{"title":"Automorphism groups of affine varieties consisting of algebraic elements","authors":"Alexander Perepechko, Andriy Regeta","doi":"10.1090/proc/16759","DOIUrl":"https://doi.org/10.1090/proc/16759","url":null,"abstract":"Given an affine algebraic variety <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\"> <mml:semantics> <mml:mi>X</mml:mi> <mml:annotation encoding=\"application/x-tex\">X</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove that if the neutral component <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"normal upper A normal u normal t Superscript ring Baseline left-parenthesis upper X right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"normal\">A</mml:mi> <mml:mi mathvariant=\"normal\">u</mml:mi> <mml:mi mathvariant=\"normal\">t</mml:mi> </mml:mrow> <mml:mo>∘</mml:mo> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>X</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathrm {Aut}^circ (X)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> of the automorphism group consists of algebraic elements, then it is nested, i.e., is a direct limit of algebraic subgroups. This improves our earlier result (see Perepechko and Regeta [Transform. Groups 28 (2023), pp. 401–412]). To prove it, we obtain the following fact. If a connected ind-group <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper G\"> <mml:semantics> <mml:mi>G</mml:mi> <mml:annotation encoding=\"application/x-tex\">G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> contains a closed connected nested ind-subgroup <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H subset-of upper G\"> <mml:semantics> <mml:mrow> <mml:mi>H</mml:mi> <mml:mo>⊂</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Hsubset G</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, and for any <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g element-of upper G\"> <mml:semantics> <mml:mrow> <mml:mi>g</mml:mi> <mml:mo>∈</mml:mo> <mml:mi>G</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">gin G</mml:annotation> </mml:semantics> </mml:math> </inline-formula> some positive power of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"g\"> <mml:semantics> <mml:mi>g</mml:mi> <mml:annotation encoding=\"application/x-tex\">g</mml:annotation> </mml:semantics> </mml:math> </inline-formula> belongs to <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper H\"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding=\"application/x-tex\">H</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, then <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"138 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The prime spectrum of an 𝐿-algebra 𝐿-algebra 的质谱

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16802

Wolfgang Rump, Leandro Vendramin

We prove that the lattice of ideals of an arbitrary L L -algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of L L -algebras and characterize prime ideals in topological terms.

我们证明了任意 L L -代数的理想晶格是可分配的。因此，谱理论的应用不受限制。我们还研究了 L L -代数的谱（即素理想集），并用拓扑术语描述了素理想的特征。

引用次数: 0

CR embeddings of nilpotent Lie groups 零potent Lie 群的 CR 嵌入

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16818

M. Cowling, M. Ganji, A. Ottazzi, G. Schmalz

In this note we show that a connected, simply connected nilpotent Lie group with an integrable left-invariant complex structure on a generating and suitably complemented subbundle of the tangent bundle admits a Cauchy-Riemann (CR) embedding in complex space defined by polynomials. We also show that a similar conclusion holds on suitable quotients of nilpotent Lie groups. Our results extend the CR embeddings constructed by Naruki [Publ. Res. Inst. Math. Sci. 6 (1970), pp. 113–187] in 1970. In particular, our generalisation to quotients allows us to see a class of Levi degenerate CR manifolds as quotients of nilpotent Lie groups.

在本论文中，我们证明了在切线束的生成子束上具有可积分左不变复结构的简单相连零能李群，在复空间中具有由多项式定义的考奇-黎曼（Cauchy-Riemann，CR）嵌入。我们还证明，类似的结论也适用于零potent Lie 群的适当商。我们的结果扩展了 Naruki [Publ. Res. Inst. Math. Sci.特别是，我们对商的概括使我们能够把一类 Levi 退化 CR 流形看成是无势 Lie 群的商。

引用次数: 0

Corrigendum to “A Severi type theorem for surfaces in ℙ⁶” 对 "ℙ⁶中曲面的塞维里类型定理 "的更正

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16819

Pietro De Poi, Giovanna Ilardi

In Theorem 0.1 of the paper “A Severi type theorem for surfaces in P 6 mathbb {P}^6 ” [Proc. Amer. Math. Soc. 149 (2021), pp. 591–605], we claimed to have given a complete classification of smooth surfaces in P 6 mathbb {P}^6 with one 4-secant plane through the general point of P 6 mathbb {P}^6 , but the classification is still incomplete.

在论文 "A Severi type theorem for surfaces in P 6 mathbb {P}^6 "[Proc. Amer. Math. Soc. 149 (2021), pp.

{"title":"Corrigendum to “A Severi type theorem for surfaces in ℙ⁶”","authors":"Pietro De Poi, Giovanna Ilardi","doi":"10.1090/proc/16819","DOIUrl":"https://doi.org/10.1090/proc/16819","url":null,"abstract":"In Theorem 0.1 of the paper “A Severi type theorem for surfaces in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P Superscript 6\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>6</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {P}^6</mml:annotation> </mml:semantics> </mml:math> </inline-formula>” [Proc. Amer. Math. Soc. 149 (2021), pp. 591–605], we claimed to have given a complete classification of smooth surfaces in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P Superscript 6\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>6</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {P}^6</mml:annotation> </mml:semantics> </mml:math> </inline-formula> with one 4-secant plane through the general point of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper P Superscript 6\"> <mml:semantics> <mml:msup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mn>6</mml:mn> </mml:msup> <mml:annotation encoding=\"application/x-tex\">mathbb {P}^6</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, but the classification is still incomplete.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"31 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140938929","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Geometry of spectral bounds of curves of unitary operators 单元算子曲线谱边界的几何性质

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16815

Martin Miglioli

This article presents a new proof of a theorem concerning bounds of the spectrum of the product of unitary operators and a generalization for differentiable curves of this theorem. The proofs involve metric geometric arguments in the group of unitary operators and the sphere where these operators act.

本文提出了关于单元算子乘积谱边界定理的新证明，以及该定理在可微分曲线上的广义化。证明涉及单元算子组和这些算子作用的球面中的度量几何论证。

引用次数: 0

The geproci property in positive characteristic 正特征中的 geproci 性质

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16809

Jake Kettinger

The geproci property is a recent development in the world of geometry. We call a set of points Z ⊆ P k 3 Zsubseteq mathbb {P}_k^3 an ( a , b ) (a,b) -geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point P P to a plane is a complete intersection of curves of degrees a ≤ b aleq b . Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids.

In this paper, based partly on the author’s thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids.

geproci 属性是几何学领域的最新发展。如果一个点集 Z ⊆ P k 3 Zsubseteq mathbb {P}_k^3 是一个（a , b ）（a,b）-geproci 集（GEneral PROjection is a Complete Intersection 的缩写），而它从一般点 P P 到平面的投影是 a≤b aleq b 的度数的曲线的完全交集，我们就称这个点集为 geproci 集。早在 2011 年，人们就知道了被称为网格的非enerate 例子。2018 年首次描述了非enerate 非网格，在特征 0 下工作。几乎所有这些新例子都属于一种特殊类型，称为半网格。在本文中，我们部分基于作者的论文，利用正特征几何的一个特点，给出了产生geproci半网格和非半网格的新方法。

{"title":"The geproci property in positive characteristic","authors":"Jake Kettinger","doi":"10.1090/proc/16809","DOIUrl":"https://doi.org/10.1090/proc/16809","url":null,"abstract":"The geproci property is a recent development in the world of geometry. We call a set of points <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Z subset-of-or-equal-to double-struck upper P Subscript k Superscript 3\"> <mml:semantics> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>⊆</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi mathvariant=\"double-struck\">P</mml:mi> </mml:mrow> <mml:mi>k</mml:mi> <mml:mn>3</mml:mn> </mml:msubsup> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">Zsubseteq mathbb {P}_k^3</mml:annotation> </mml:semantics> </mml:math> </inline-formula> an <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis a comma b right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mi>a</mml:mi> <mml:mo>,</mml:mo> <mml:mi>b</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">(a,b)</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-geproci set (for GEneral PROjection is a Complete Intersection) if its projection from a general point <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper P\"> <mml:semantics> <mml:mi>P</mml:mi> <mml:annotation encoding=\"application/x-tex\">P</mml:annotation> </mml:semantics> </mml:math> </inline-formula> to a plane is a complete intersection of curves of degrees <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"a less-than-or-equal-to b\"> <mml:semantics> <mml:mrow> <mml:mi>a</mml:mi> <mml:mo>≤</mml:mo> <mml:mi>b</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">aleq b</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Nondegenerate examples known as grids have been known since 2011. Nondegenerate nongrids were first described in 2018, working in characteristic 0. Almost all of these new examples are of a special kind called half grids. In this paper, based partly on the author’s thesis, we use a feature of geometry in positive characteristic to give new methods of producing geproci half grids and non-half grids.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"226 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Spectral stability under removal of small segments 去除小段后的频谱稳定性

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16813

Xiang He

In the present paper, we deepen the works of L. Abatangelo, V. Felli, L. Hillairet and C. Léna on the asymptotic estimates of the eigenvalue variation under removal of segments from the domain in R 2 mathbb {R}^2 . We get a sharp asymptotic estimate when the eigenvalue is simple and the removed segment is tangent to a nodal line of the associated eigenfunction. Moreover, we extend their results to the case when the eigenvalue is not simple.

在本文中，我们深化了 L. Abatangelo、V. Felli、L. Hillairet 和 C. Léna 关于从 R 2 mathbb {R}^2 中的域中移除线段时特征值变化的渐近估计的研究。当特征值简单且移除的线段与相关特征函数的节点线相切时，我们得到了一个尖锐的渐近估计值。此外，我们还将他们的结果扩展到了特征值不简单的情况。

引用次数: 0

Notes on noncommutative ergodic theorems 非交换遍历定理注释

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16807

Semyon Litvinov

Given a semifinite von Neumann algebra <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper M"> <mml:semantics> <mml:mrow> <mml:mi mathvariant="script">M</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">mathcal M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> equipped with a faithful normal semifinite trace <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="tau"> <mml:semantics> <mml:mi>τ</mml:mi> <mml:annotation encoding="application/x-tex">tau</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove that the spaces <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript 0 Baseline left-parenthesis script upper M comma tau right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="script">M</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">L^0(mathcal M,tau )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper R Subscript tau"> <mml:semantics> <mml:msub> <mml:mrow> <mml:mi mathvariant="script">R</mml:mi> </mml:mrow> <mml:mi>τ</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">mathcal R_tau</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are complete with respect to pointwise—almost uniform and bilaterally almost uniform—convergences in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript 0 Baseline left-parenthesis script upper M comma tau right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="script">M</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">L^0(mathcal M,tau )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Then we show that the pointwise Cauchy property for a special class of nets of linear operators in the space <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper L Superscript 1 Baseline left-parenthesis script upper M comma tau right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mrow> <mml:mi mathvariant="script">M</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:ann

给定一个半有穷冯-诺依曼代数 M （M mathcal M）配有一个忠实的正态半有穷迹线 τ tau，我们证明空间 L 0 ( M , τ ) L^0(mathcal M,tau ) 和 R τ mathcal R_tau 就 L 0 ( M , τ ) L^0(mathcal M,tau ) 中的点-几乎均匀和双边几乎均匀-转换而言是完备的。然后，我们证明在空间 L 1 ( M , τ ) L^1(mathcal M., tau ) 中线性算子网的一类特殊的 Pointwise Cauchy 属性可以扩展到 L 0 ( M , τ ) L^0(mathcal M., tau ) 中、tau ) 可以扩展到在任何完全对称空间 E ⊂ R τ Esubset mathcal R_tau 中这类网的点收敛，特别是在任何空间 L p ( M , τ ) L^p(mathcal M,tau ) , 1 ≤ p >；∞ 1leq p>infty .讨论了这些结果在非交换遍历理论中的一些应用。

{"title":"Notes on noncommutative ergodic theorems","authors":"Semyon Litvinov","doi":"10.1090/proc/16807","DOIUrl":"https://doi.org/10.1090/proc/16807","url":null,"abstract":"Given a semifinite von Neumann algebra <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper M\"> <mml:semantics> <mml:mrow> <mml:mi mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">mathcal M</mml:annotation> </mml:semantics> </mml:math> </inline-formula> equipped with a faithful normal semifinite trace <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"tau\"> <mml:semantics> <mml:mi>τ</mml:mi> <mml:annotation encoding=\"application/x-tex\">tau</mml:annotation> </mml:semantics> </mml:math> </inline-formula>, we prove that the spaces <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0 Baseline left-parenthesis script upper M comma tau right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">L^0(mathcal M,tau )</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"script upper R Subscript tau\"> <mml:semantics> <mml:msub> <mml:mrow> <mml:mi mathvariant=\"script\">R</mml:mi> </mml:mrow> <mml:mi>τ</mml:mi> </mml:msub> <mml:annotation encoding=\"application/x-tex\">mathcal R_tau</mml:annotation> </mml:semantics> </mml:math> </inline-formula> are complete with respect to pointwise—almost uniform and bilaterally almost uniform—convergences in <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 0 Baseline left-parenthesis script upper M comma tau right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>0</mml:mn> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">L^0(mathcal M,tau )</mml:annotation> </mml:semantics> </mml:math> </inline-formula>. Then we show that the pointwise Cauchy property for a special class of nets of linear operators in the space <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper L Superscript 1 Baseline left-parenthesis script upper M comma tau right-parenthesis\"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>L</mml:mi> <mml:mn>1</mml:mn> </mml:msup> <mml:mo stretchy=\"false\">(</mml:mo> <mml:mrow> <mml:mi mathvariant=\"script\">M</mml:mi> </mml:mrow> <mml:mo>,</mml:mo> <mml:mi>τ</mml:mi> <mml:mo stretchy=\"false\">)</mml:mo> </mml:mrow> <mml:ann","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"128 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Sobol’ sequence is not quasi-uniform in dimension 2 索布尔序列在维 2 中不是准均匀的

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16816

Takashi Goda

Are common quasi-Monte Carlo sequences quasi-uniform? While this question remains widely open, in this short note, we prove that the two-dimensional Sobol’ sequence is not quasi-uniform. This result partially answers an unsolved problem of Sobol’ and Shukhman [Math. Comput. Simulation 75 (2007), pp. 80–86] in a negative manner.

常见的准蒙特卡罗序列是准均匀的吗？尽管这个问题仍然悬而未决，但在这篇短文中，我们证明了二维索博尔序列不是准均匀序列。这一结果以否定的方式部分回答了 Sobol' 和 Shukhman [Math. Comput. Simulation 75 (2007), pp.

引用次数: 0

Some 𝑞-identities derived by the ordinary derivative operator 由普通导数算子推导出的一些Δ常数

IF 1 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society

Pub Date : 2024-02-29 DOI: 10.1090/proc/16817

Jin Wang, Ruiqi Ruan

In this paper, we investigate applications of the ordinary derivative operator, instead of the q q -derivative operator, to the theory of q q -series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the q q -binomial theorem, Ramanujan’s 1 ψ 1 {}_1psi _1 formula, the quintuple product identity, Gasper’s q q -Clausen product formula, and Rogers’ 6 ϕ 5 {}_6phi _5 formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein’s theorem on Lambert series.

本文研究了普通导数算子而非 q q -导数算子在 q q -数列理论中的应用。作为主要成果，我们建立了许多新的求和与变换公式，它们与一些著名公式密切相关，如 q q -二项式定理、Ramanujan 的 1 ψ 1 {}_1psi _1 公式、五次乘积同一性、Gasper 的 q q -Clausen 乘积公式和 Rogers 的 6 ϕ 5 {}_6phi _5 公式等。在这些结果中，有罗杰斯-拉马努扬特性的有限形式，也有爱森斯坦兰伯特级数定理的捷径。

{"title":"Some 𝑞-identities derived by the ordinary derivative operator","authors":"Jin Wang, Ruiqi Ruan","doi":"10.1090/proc/16817","DOIUrl":"https://doi.org/10.1090/proc/16817","url":null,"abstract":"In this paper, we investigate applications of the ordinary derivative operator, instead of the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-derivative operator, to the theory of <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-binomial theorem, Ramanujan’s <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Subscript 1 Baseline psi 1\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow> </mml:mrow> <mml:mn>1</mml:mn> </mml:msub> <mml:msub> <mml:mi>ψ</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">{}_1psi _1</mml:annotation> </mml:semantics> </mml:math> </inline-formula> formula, the quintuple product identity, Gasper’s <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"q\"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding=\"application/x-tex\">q</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-Clausen product formula, and Rogers’ <inline-formula content-type=\"math/mathml\"> <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"Subscript 6 Baseline phi 5\"> <mml:semantics> <mml:mrow> <mml:msub> <mml:mrow> </mml:mrow> <mml:mn>6</mml:mn> </mml:msub> <mml:msub> <mml:mi>ϕ</mml:mi> <mml:mn>5</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding=\"application/x-tex\">{}_6phi _5</mml:annotation> </mml:semantics> </mml:math> </inline-formula> formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein’s theorem on Lambert series.","PeriodicalId":20696,"journal":{"name":"Proceedings of the American Mathematical Society","volume":"56 73 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141516774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

首页上一页

下一页尾页

类型

全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

数据库

全部 ACS Publications Elsevier ieeexplore Springer The Royal Society of Chemistry Wiley

期刊

Proceedings of the American Mathematical Society

全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.

﹀