Infinite matrices and their finite sections : an introduction to the limit operator method /

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Bibliographic Details
Author / Creator:Lindner, Marko, 1973-
Imprint:Basel ; Boston : Birkhäuser, c2006.
Description:1 online resource (xv, 191 p.) : ill.
Language:English
Series:Frontiers in mathematics
Frontiers in mathematics.
Subject:
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/8880540
Hidden Bibliographic Details
ISBN:9783764377670
3764377674
3764377666
9783764377663
Notes:Includes bibliographical references (p. [185]-191) and index.
Description based on print version record.
Other form:Print version: Lindner, Marko, 1973- Infinite matrices and their finite sections. Basel ; Boston : Birkhäuser, c2006 3764377666 9783764377663
Description
Summary:In this book we are concerned with the study of a certain class of in?nite matrices and two important properties of them: their Fredholmness and the stability of the approximation by their ?nite truncations. Let us take these two properties as a starting point for the big picture that shall be presented in what follows. Stability Fredholmness We think of our in?nite matrices as bounded linear operators on a Banach space E of two-sided in?nite sequences. Probably the simplest case to start with 2 +? is the space E = of all complex-valued sequences u=(u ) for which m m=?? 2 |u | is summable over m? Z. m Theclassofoperatorsweareinterestedinconsistsofthoseboundedandlinear operatorsonE whichcanbeapproximatedintheoperatornormbybandmatrices. We refer to them as band-dominated operators. Of course, these considerations 2 are not limited to the space E = . We will widen the selection of the underlying space E in three directions: p * We pass to the classical sequence spaces with 1? p??. n * Our elements u=(u )? E have indices m? Z rather than just m? Z. m * We allow values u in an arbitrary ?xed Banach spaceX rather than C.
Physical Description:1 online resource (xv, 191 p.) : ill.
Bibliography:Includes bibliographical references (p. [185]-191) and index.
ISBN:9783764377670
3764377674
3764377666
9783764377663