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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.
| Autorius: | Marko Lindner |
| Serija: | Frontiers in Mathematics |
| Leidėjas: | Birkhäuser Basel |
| Išleidimo metai: | 2006 |
| Knygos puslapių skaičius: | 212 |
| ISBN-10: | 3764377666 |
| ISBN-13: | 9783764377663 |
| Formatas: | 244 x 170 x 12 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
Parašykite atsiliepimą apie „Infinite Matrices and their Finite Sections: An Introduction to the Limit Operator Method“
