TY  - BOOK
AU  - 
ED  - SpringerLink (Online service)
TI  - Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method 
T2  - Frontiers in Mathematics,
SN  - 9783764377670
AV  - QA319-329.9 
U1  - 515.7 23
PY  - 2006///
CY  - Basel
PB  - Birkhuser Basel
KW  - Mathematics
KW  - Matrix theory
KW  - Functional analysis
KW  - Numerical analysis
KW  - Functional Analysis
KW  - Linear and Multilinear Algebras, Matrix Theory
KW  - Numerical Analysis
N1  - Preliminaries -- Invertibility at Infinity -- Limit Operators -- Stability of the Finite Section Method
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-7643-7767-0
ER  -