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 operatorson E 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 space X rather than C.
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विषयसूची
Preliminaries.- Invertibility at Infinity.- Limit Operators.- Stability of the Finite Section Method.
भाषा अंग्रेज़ी ● स्वरूप PDF ● पेज 191 ● ISBN 9783764377670 ● फाइल का आकार 1.9 MB ● प्रकाशक Springer Basel ● शहर Basel ● देश CH ● प्रकाशित 2006 ● डाउनलोड करने योग्य 24 महीने ● मुद्रा EUR ● आईडी 2205724 ● कॉपी सुरक्षा सामाजिक DRM
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