加权bergman空间上的Fredholm toeplitz算子

Q4 Mathematics Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2021-01-01 DOI:10.56082/annalsarscimath.2022.1-2.178

N. Das, Swarupa Roy

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引用次数: 0

摘要

在本文中，我们证明了如果φ∈(L2h(dAα))⊥∩L∞(D)且ranget (α)φ是闭合的，那么Toeplitz算子T(α)φ∈L∈L2a(dAα) φ是索引为零的Fredholm算子，并且T(α)φ不是有限秩的。并给出了该结果的几个应用实例。我们进一步证明，如果φ∈L∞Mn(D)满足Tφ为Fredholm且指标为0，则存在ψ∈En×n= E⊗Mn，使得Tφ+δψ对所有足够小的非零δ可逆。这里E是L∞(D)的一个总的子空间，Mnis是所有n × n个复元素矩阵的集合。

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FREDHOLM TOEPLITZ OPERATORS ON THE WEIGHTED BERGMAN SPACES

In this paper we have shown that if φ ∈ (L2h(dAα))⊥∩ L∞(D) andRangeT(α)φis closed, then the Toeplitz operator T(α)φ∈ LL2a(dAα)is a Fredholm operator of index zero and T(α)φis not of ﬁnite rank.Several applications of the result were also obtained. We further showthat if φ ∈ L∞Mn(D) is such that Tφis Fredholm and of index zero inLL2,Cna(dAα)then there exists ψ ∈ En×n= E ⊗Mnsuch that Tφ+δψis invertible for all suﬃciently small nonzero δ. Here E is a total sub-space of L∞(D) and Mnis the set of all n × n matrices with complexentries.

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.