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

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• 作者：Markus Seidel
• 关键词：47A53 ; 47B07 ; 46E40 ; 47B36 ; 47L80
• 刊名：Linear Algebra and its Applications
• 出版年：15 March, 2014
• 年：2014
• 卷：445
• 期：Complete
• 页码：373-394
• 全文大小：410 K

文摘

This paper presents the Fredholm theory on -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 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.