Infinite matrices and their finite sections : an introduction to the limit operator method /
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| Author / Creator: | Lindner, Marko, 1973- |
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| 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 |
| 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. |
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| Physical Description: | 1 online resource (xv, 191 p.) : ill. |
| Bibliography: | Includes bibliographical references (p. [185]-191) and index. |
| ISBN: | 9783764377670 3764377674 3764377666 9783764377663 |