Infinite Matrices and their Finite Sections : An Introduction to the Limit Operator Method / by Marko Lindner
(Frontiers in Mathematics)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | Basel : Birkhäuser Basel |
| 出版年 | 2006 |
| 本文言語 | 英語 |
| 大きさ | XV, 191 p. 12 illus : online resource |
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| 内容注記 | Preliminaries Invertibility at Infinity Limit Operators Stability of the Finite Section Method |
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| 一般注記 | 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 |
| 著者標目 | *Lindner, Marko author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Matrix theory LCSH:Algebra LCSH:Functional analysis LCSH:Numerical analysis FREE:Mathematics FREE:Functional Analysis FREE:Linear and Multilinear Algebras, Matrix Theory FREE:Numerical Analysis |
| 分 類 | DC23:515.7 |
| 巻冊次 | ISBN:9783764377670 
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| ISBN | 9783764377670 |
| URL | http://dx.doi.org/10.1007/978-3-7643-7767-0 |
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