Marko Lindner

(Author)

Infinite Matrices and Their Finite Sections: An Introduction to the Limit Operator MethodPaperback, 16 August 2006

Infinite Matrices and Their Finite Sections: An Introduction to the Limit Operator Method
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Part of Series
Frontiers in Mathematics
Print Length
191 pages
Language
English
Publisher
Birkhauser
Date Published
16 Aug 2006
ISBN-10
3764377666
ISBN-13
9783764377663

Description

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.

Product Details

Author:
Marko Lindner
Book Format:
Paperback
Country of Origin:
DE
Date Published:
16 August 2006
Dimensions:
23.62 x 16.76 x 1.27 cm
ISBN-10:
3764377666
ISBN-13:
9783764377663
Language:
English
Location:
Basel
Pages:
191
Publisher:
Weight:
385.55 gm

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