Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method
In this book we are concerned with the study of a certain class of inflnite matrices and two important properties of them: their Fredholmness and the stability of the approximation by theirfinite 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 inflnite matrices as bounded linear operators on a Banach space E of two-sided inflnite 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.
1111332750
Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method
In this book we are concerned with the study of a certain class of inflnite matrices and two important properties of them: their Fredholmness and the stability of the approximation by theirfinite 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 inflnite matrices as bounded linear operators on a Banach space E of two-sided inflnite 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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Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method
191
Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method
191Paperback(2006)
$59.99
59.99
In Stock
Product Details
| ISBN-13: | 9783764377663 |
|---|---|
| Publisher: | Birkh�user Basel |
| Publication date: | 09/25/2006 |
| Series: | Frontiers in Mathematics |
| Edition description: | 2006 |
| Pages: | 191 |
| Product dimensions: | 6.69(w) x 9.45(h) x 0.02(d) |
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