Fredholm theory for band-dominated and related operators: A survey

被引：21

作者：

Seidel, Markus ^{[1
]}

机构：

[1] Tech Univ Chemnitz, Fak Math, D-09107 Chemnitz, Germany

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 445卷

关键词：

Fredholm theory; Limit operator; Band-dominated operator; Approximate identity; FINITE SECTION METHOD; BANACH-ALGEBRAS; LIMIT OPERATORS; SEQUENCES; INDEX; SPACE;

D O I：

10.1016/j.laa.2013.11.048

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper presents the Fredholm theory on l(p)-spaces for band-dominated operators and important subclasses, such as operators in the Wiener algebra. It particularly closes several gaps in the previously known results for the case p = infinity and addresses the open questions raised by Chandler-Wilde and Lindner in [S.N. Chandler-Wilde, M. Lindner, Limit operators, collective compactness and the spectral theory of infinite matrices, Mem. Amer. Math. Soc. 210 (989) (2011)]. The main tools are provided by the limit operator method and an algebraic framework for the description and adaption of Fredholmness and convergence. A comprehensive overview of this approach is given. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：373 / 394

页数：22

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