| Infinite Matrices and Their Finite Sections: An Introduction to the Limit Operator Method Contributor(s): Lindner, Marko (Author) |
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ISBN: 3764377666 ISBN-13: 9783764377663 Publisher: Birkhauser OUR PRICE: $56.99 Product Type: Paperback - Other Formats Published: August 2006 |
| Additional Information |
| BISAC Categories: - Mathematics | Matrices - Mathematics | Functional Analysis - Mathematics | Numerical Analysis |
| Dewey: 515.724 |
| LCCN: 2006049901 |
| Series: Frontiers in Mathematics |
| Physical Information: 0.5" H x 6.6" W x 9.3" (0.85 lbs) 191 pages |
| Descriptions, Reviews, Etc. |
| Publisher 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. |