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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Infinite Matrices and Their Finite Sections: An Introduction to the Limit Operator Method

Infinite Matrices and Their Finite Sections: An Introduction to the Limit Operator Method

Lindner, Marko

Paperback

Series: Frontiers in Mathematics

General Mathematics

ISBN10: 3764377666
ISBN13: 9783764377663
Publisher: Birkhauser
Published: Aug 16 2006
Pages: 191
Weight: 0.85
Height: 0.50 Width: 6.60 Depth: 9.30
Language: English
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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