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
收藏
页码：373 / 394
页数：22
相关论文
共 50 条
12345