K-Theory for Operator Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1986
|
| Schriftenreihe: | Mathematical Sciences Research Institute Publications
5 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text |
| Beschreibung: | 1 Online-Ressource (VII, 337p) |
| ISBN: | 9781461395720 9781461395744 |
| ISSN: | 0940-4740 |
| DOI: | 10.1007/978-1-4613-9572-0 |
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| 500 | |a K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text | ||
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Datensatz im Suchindex
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| author | Blackadar, Bruce |
| author_facet | Blackadar, Bruce |
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| ctrlnum | (OCoLC)906698638 (DE-599)BVBBV042420803 |
| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.2 |
| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4613-9572-0 |
| format | Electronic eBook |
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| id | DE-604.BV042420803 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:07Z |
| institution | BVB |
| isbn | 9781461395720 9781461395744 |
| issn | 0940-4740 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027856220 |
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| physical | 1 Online-Ressource (VII, 337p) |
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| spelling | Blackadar, Bruce Verfasser aut K-Theory for Operator Algebras by Bruce Blackadar New York, NY Springer New York 1986 1 Online-Ressource (VII, 337p) txt rdacontent c rdamedia cr rdacarrier Mathematical Sciences Research Institute Publications 5 0940-4740 K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact that the whole subject is only about a decade old, operator K -theory has now reached a state of relative stability. While there will undoubtedly be many more revolutionary developments and applications in the future, it appears the basic theory has more or less reached a "final form." But because of the newness of the theory, there has so far been no comprehensive treatment of the subject. It is the ambitious goal of these notes to fill this gap. We will develop the K -theory of Banach algebras, the theory of extensions of C*-algebras, and the operator K -theory of Kasparov from scratch to its most advanced aspects. We will not treat applications in detail; however, we will outline the most striking of the applications to date in a section at the end, as well as mentioning others at suitable points in the text Mathematics Algebraic topology Algebraic Topology Mathematik K-Theorie (DE-588)4033335-8 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 gnd rswk-swf Operatoralgebra (DE-588)4129366-6 s K-Theorie (DE-588)4033335-8 s 1\p DE-604 https://doi.org/10.1007/978-1-4613-9572-0 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Blackadar, Bruce K-Theory for Operator Algebras Mathematics Algebraic topology Algebraic Topology Mathematik K-Theorie (DE-588)4033335-8 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| subject_GND | (DE-588)4033335-8 (DE-588)4129366-6 |
| title | K-Theory for Operator Algebras |
| title_auth | K-Theory for Operator Algebras |
| title_exact_search | K-Theory for Operator Algebras |
| title_full | K-Theory for Operator Algebras by Bruce Blackadar |
| title_fullStr | K-Theory for Operator Algebras by Bruce Blackadar |
| title_full_unstemmed | K-Theory for Operator Algebras by Bruce Blackadar |
| title_short | K-Theory for Operator Algebras |
| title_sort | k theory for operator algebras |
| topic | Mathematics Algebraic topology Algebraic Topology Mathematik K-Theorie (DE-588)4033335-8 gnd Operatoralgebra (DE-588)4129366-6 gnd |
| topic_facet | Mathematics Algebraic topology Algebraic Topology Mathematik K-Theorie Operatoralgebra |
| url | https://doi.org/10.1007/978-1-4613-9572-0 |
| work_keys_str_mv | AT blackadarbruce ktheoryforoperatoralgebras |