Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287845
Eder Kikianty
Angular equivalence of norms, introduced by Kikianty and Sinnamon (2017), is a notion of norm equivalence that is more attuned to the geometry of the norms. For certain geometrical properties and t...
{"title":"Towards a geometrical equivalence of norms","authors":"Eder Kikianty","doi":"10.2989/16073606.2023.2287845","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287845","url":null,"abstract":"Angular equivalence of norms, introduced by Kikianty and Sinnamon (2017), is a notion of norm equivalence that is more attuned to the geometry of the norms. For certain geometrical properties and t...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"85 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140076489","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287815
Karim Boulabiar, Rawaa Hajji
Let L be a truncated Archimedean vector lattice whose truncation is denoted by *. In a recent paper, we proved that there exists a locally compact Hausdorff space X such that L is a lattice isomorph...
设 L 是一个截断的阿基米德向量网格，其截断数用 * 表示。在最近的一篇论文中，我们证明了存在一个局部紧凑的豪斯多尔空间X，使得L是一个同构的网格。
{"title":"Truncated vector lattices: A Maeda-Ogasawara type representation","authors":"Karim Boulabiar, Rawaa Hajji","doi":"10.2989/16073606.2023.2287815","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287815","url":null,"abstract":"Let L be a truncated Archimedean vector lattice whose truncation is denoted by *. In a recent paper, we proved that there exists a locally compact Hausdorff space X such that L is a lattice isomorph...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"107 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140073404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287814
Aleksey Ber, Vladimir Chilin, Fedor Sukochev
We show that any nonexpansive derivation on a subalgebra of a dis-jointly complete commutative regular algebra extends up to a derivation on . For an algebra of functions , continuous on a dense ...
{"title":"Derivations in disjointly complete commutative regular algebras","authors":"Aleksey Ber, Vladimir Chilin, Fedor Sukochev","doi":"10.2989/16073606.2023.2287814","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287814","url":null,"abstract":"We show that any nonexpansive derivation on a subalgebra of a dis-jointly complete commutative regular algebra extends up to a derivation on . For an algebra of functions , continuous on a dense ...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"2016 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140107107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287846
Anatoly G. Kusraev, Semën S. Kutateladze
The aim of the present article is to extend the Stone-Weierstrass theorem to functions ranging in a lattice normed space and admitting order rather than topological approximation. We proceed with t...
本文旨在将斯通-韦尔斯特拉斯定理扩展到网格规范空间中的函数，并允许有序而非拓扑逼近。我们从...
{"title":"Stone-Weierstrass approximation revisited","authors":"Anatoly G. Kusraev, Semën S. Kutateladze","doi":"10.2989/16073606.2023.2287846","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287846","url":null,"abstract":"The aim of the present article is to extend the Stone-Weierstrass theorem to functions ranging in a lattice normed space and admitting order rather than topological approximation. We proceed with t...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140073530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287831
Jochen Glück, Michael Kaplin
Relatively uniformly continuous (ruc) semigroups were recently introduced and studied by Kandic, Kramar-Fijavž, and the second-named author, in order to make the theory of one-parameter operator se...
{"title":"Order boundedness and order continuity properties of positive operator semigroups","authors":"Jochen Glück, Michael Kaplin","doi":"10.2989/16073606.2023.2287831","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287831","url":null,"abstract":"Relatively uniformly continuous (ruc) semigroups were recently introduced and studied by Kandic, Kramar-Fijavž, and the second-named author, in order to make the theory of one-parameter operator se...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"39 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140073575","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287823
Ben de Pagter, Werner J. Ricker
It is known that if L is a Dedekind complete Riesz space and (Ω, Σ) is a measurable space, then the partially ordered linear space of all L-valued, finitely additive and order bounded vector measur...
众所周知，如果 L 是一个 Dedekind 完全 Riesz 空间，(Ω, Σ) 是一个可测空间，那么所有 L 值、有限相加和有序有界向量测量的部分有序线性空间...
{"title":"The modulus of a vector measure","authors":"Ben de Pagter, Werner J. Ricker","doi":"10.2989/16073606.2023.2287823","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287823","url":null,"abstract":"It is known that if L is a Dedekind complete Riesz space and (Ω, Σ) is a measurable space, then the partially ordered linear space of all L-valued, finitely additive and order bounded vector measur...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140073592","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287853
Youssef Azouzi, Youssef Nasri
We introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectation operator. This allows us to study discrete ...
{"title":"Generating functions in Riesz spaces","authors":"Youssef Azouzi, Youssef Nasri","doi":"10.2989/16073606.2023.2287853","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287853","url":null,"abstract":"We introduce and study the concept of generating function for natural elements in a Dedekind complete Riesz space equipped with a conditional expectation operator. This allows us to study discrete ...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"32 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140073563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287829
R. Drnovšek, M. Kandić
This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order...
{"title":"On the diagonal of Riesz operators on Banach lattices","authors":"R. Drnovšek, M. Kandić","doi":"10.2989/16073606.2023.2287829","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287829","url":null,"abstract":"This paper extends the well-known Ringrose theory for compact operators to polynomially Riesz operators on Banach spaces. The particular case of an ideal-triangularizable Riesz operator on an order...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"42 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140073403","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287847
Louis Labuschagne
We revisit the generalisation of Calderon’s Transfer Principle as espoused in [7]. This principle is used to generate weak type maximal inequalities for ergodic operators in the setting of σ-compac...
{"title":"Weak and strong type inequalities for Orlicz spaces","authors":"Louis Labuschagne","doi":"10.2989/16073606.2023.2287847","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287847","url":null,"abstract":"We revisit the generalisation of Calderon’s Transfer Principle as espoused in [7]. This principle is used to generate weak type maximal inequalities for ergodic operators in the setting of σ-compac...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"37 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140073397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-03-07DOI: 10.2989/16073606.2023.2287839
Francisco L. Hernández, César Ruiz, Mauro Sanchiz
We give two weak compactness Andô type criteria in variable exponent Lebesgue spaces Lp(·) (Ω) on infinite measures. This extends some results of [13] given in the case of finite measures. Spaces L...
{"title":"Remarks on weak compactness criteria in variable exponent Lebesgue spaces","authors":"Francisco L. Hernández, César Ruiz, Mauro Sanchiz","doi":"10.2989/16073606.2023.2287839","DOIUrl":"https://doi.org/10.2989/16073606.2023.2287839","url":null,"abstract":"We give two weak compactness Andô type criteria in variable exponent Lebesgue spaces Lp(·) (Ω) on infinite measures. This extends some results of [13] given in the case of finite measures. Spaces L...","PeriodicalId":49652,"journal":{"name":"Quaestiones Mathematicae","volume":"21 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140073548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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