Limit Operators and Their Applications in Operator Theory:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2004
|
| Schriftenreihe: | Operator Theory: Advances and Applications
150 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | This text has two goals. It describes a topic: band and band-dominated operators and their Fredholm theory, and it introduces a method to study this topic: limit operators. Band-dominated operators. Let H = [2(Z) be the Hilbert space of all squared summable functions x : Z -+ Xi provided with the norm 2 2 X IIxl1 :=L I iI . iEZ It is often convenient to think of the elements x of [2(Z) as two-sided infinite sequences (Xi)iEZ. The standard basis of [2(Z) is the family of sequences (ei)iEZ where ei = (. . . ,0,0, 1,0,0, . . . ) with the 1 standing at the ith place. Every bounded linear operator A on H can be described by a two-sided infinite matrix (aij)i,jEZ with respect to this basis, where aij = (Aej, ei)' The band operators on H are just the operators with a matrix representation of finite band-width, i. e. , the operators for which aij = 0 whenever Ii - jl > k for some k. Operators which are in the norm closure ofthe algebra of all band operators are called band-dominated. Needless to say that band and band dominated operators appear in numerous branches of mathematics. Archetypal examples come from discretizations of partial differential operators. It is easy to check that every band operator can be uniquely written as a finite sum L dkVk where the d are multiplication operators (i. e |
| Beschreibung: | 1 Online-Ressource (XV, 392 p) |
| ISBN: | 9783034879118 9783034896191 |
| DOI: | 10.1007/978-3-0348-7911-8 |
Internformat
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| 245 | 1 | 0 | |a Limit Operators and Their Applications in Operator Theory |c by Vladimir Rabinovich, Bernd Silbermann, Steffen Roch |
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Datensatz im Suchindex
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| author | Rabinovich, Vladimir |
| author_facet | Rabinovich, Vladimir |
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| author_sort | Rabinovich, Vladimir |
| author_variant | v r vr |
| building | Verbundindex |
| bvnumber | BV042421983 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.724 |
| dewey-search | 515.724 |
| dewey-sort | 3515.724 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-0348-7911-8 |
| format | Electronic eBook |
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| id | DE-604.BV042421983 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:10Z |
| institution | BVB |
| isbn | 9783034879118 9783034896191 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857400 |
| oclc_num | 1184423403 |
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| physical | 1 Online-Ressource (XV, 392 p) |
| psigel | ZDB-2-SMA ZDB-2-BAE ZDB-2-SMA_Archive |
| publishDate | 2004 |
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| series2 | Operator Theory: Advances and Applications |
| spelling | Rabinovich, Vladimir Verfasser aut Limit Operators and Their Applications in Operator Theory by Vladimir Rabinovich, Bernd Silbermann, Steffen Roch Basel Birkhäuser Basel 2004 1 Online-Ressource (XV, 392 p) txt rdacontent c rdamedia cr rdacarrier Operator Theory: Advances and Applications 150 This text has two goals. It describes a topic: band and band-dominated operators and their Fredholm theory, and it introduces a method to study this topic: limit operators. Band-dominated operators. Let H = [2(Z) be the Hilbert space of all squared summable functions x : Z -+ Xi provided with the norm 2 2 X IIxl1 :=L I iI . iEZ It is often convenient to think of the elements x of [2(Z) as two-sided infinite sequences (Xi)iEZ. The standard basis of [2(Z) is the family of sequences (ei)iEZ where ei = (. . . ,0,0, 1,0,0, . . . ) with the 1 standing at the ith place. Every bounded linear operator A on H can be described by a two-sided infinite matrix (aij)i,jEZ with respect to this basis, where aij = (Aej, ei)' The band operators on H are just the operators with a matrix representation of finite band-width, i. e. , the operators for which aij = 0 whenever Ii - jl > k for some k. Operators which are in the norm closure ofthe algebra of all band operators are called band-dominated. Needless to say that band and band dominated operators appear in numerous branches of mathematics. Archetypal examples come from discretizations of partial differential operators. It is easy to check that every band operator can be uniquely written as a finite sum L dkVk where the d are multiplication operators (i. e Mathematics Operator theory Operator Theory Mathematik Operatortheorie (DE-588)4075665-8 gnd rswk-swf Operatortheorie (DE-588)4075665-8 s 1\p DE-604 Silbermann, Bernd Sonstige oth Roch, Steffen Sonstige oth https://doi.org/10.1007/978-3-0348-7911-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Rabinovich, Vladimir Limit Operators and Their Applications in Operator Theory Mathematics Operator theory Operator Theory Mathematik Operatortheorie (DE-588)4075665-8 gnd |
| subject_GND | (DE-588)4075665-8 |
| title | Limit Operators and Their Applications in Operator Theory |
| title_auth | Limit Operators and Their Applications in Operator Theory |
| title_exact_search | Limit Operators and Their Applications in Operator Theory |
| title_full | Limit Operators and Their Applications in Operator Theory by Vladimir Rabinovich, Bernd Silbermann, Steffen Roch |
| title_fullStr | Limit Operators and Their Applications in Operator Theory by Vladimir Rabinovich, Bernd Silbermann, Steffen Roch |
| title_full_unstemmed | Limit Operators and Their Applications in Operator Theory by Vladimir Rabinovich, Bernd Silbermann, Steffen Roch |
| title_short | Limit Operators and Their Applications in Operator Theory |
| title_sort | limit operators and their applications in operator theory |
| topic | Mathematics Operator theory Operator Theory Mathematik Operatortheorie (DE-588)4075665-8 gnd |
| topic_facet | Mathematics Operator theory Operator Theory Mathematik Operatortheorie |
| url | https://doi.org/10.1007/978-3-0348-7911-8 |
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