Infinite Matrices and their Finite Sections : An Introduction to the Limit Operator Method /
By: Lindner, Marko [author.].
Contributor(s): SpringerLink (Online service).
Material type:
BookSeries: Frontiers in Mathematics: Publisher: Basel : Birkhäuser Basel, 2006.Description: XV, 191 p. 12 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783764377670.Subject(s): Mathematics | Matrix theory | Algebra | Functional analysis | Numerical analysis | Mathematics | Functional Analysis | Linear and Multilinear Algebras, Matrix Theory | Numerical AnalysisDDC classification: 515.7 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
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E books
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PK Kelkar Library, IIT Kanpur | Available | EBK7982 |
Preliminaries -- Invertibility at Infinity -- Limit Operators -- Stability of the Finite Section Method.
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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