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 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 prese...
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| Glavni autor: | |
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| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
Basel :
Birkhäuser Basel
2006.
Cham : Springer Nature |
| Serija: | Frontiers in Mathematics
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| Teme: | |
| Online pristup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Bilješka: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Infinite Matrices and their Finite Sections, Texte imprimé, 9783764391539 • Infinite Matrices and their Finite Sections, Texte imprimé, 9783764377663 |
| Sažetak: | 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. |
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| Opis djela: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9783764377670 |
| ISSN: | 1660-8054 |
| Pristup: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. chttps://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |