Jordan, Real and Lie Structures in Operator Algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht
Springer Netherlands
1997
|
| Schriftenreihe: | Mathematics and Its Applications
418 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and investigation of general W* -algebras can be reduced to the case of factors. Therefore the theory of factors is one of the main tools in the structure theory of von Neumann algebras. In the middle of sixtieth Topping [To 1] and Stormer [S 2] have ini tiated the study of Jordan (non associative and real) analogues of von Neumann algebras - so called JW-algebras, i.e. real linear spaces of self adjoint opera.tors on a complex Hilbert space, which contain the identity operator 1. closed with respect to the Jordan (i.e. symmetrised) product INTRODUCTION 2 x 0 y = ~(Xy + yx) and closed in the weak operator topology. The structure of these algebras has happened to be close to the struc ture of von Neumann algebras and it was possible to apply ideas and meth ods similar to von Neumann algebras theory in the study of JW-algebras |
| Beschreibung: | 1 Online-Ressource (IX, 230 p) |
| ISBN: | 9789401586054 9789048148912 |
| DOI: | 10.1007/978-94-015-8605-4 |
Internformat
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| 245 | 1 | 0 | |a Jordan, Real and Lie Structures in Operator Algebras |c by Shavkat Ayupov, Abdugafur Rakhimov, Shukhrat Usmanov |
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| 500 | |a The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and investigation of general W* -algebras can be reduced to the case of factors. Therefore the theory of factors is one of the main tools in the structure theory of von Neumann algebras. In the middle of sixtieth Topping [To 1] and Stormer [S 2] have ini tiated the study of Jordan (non associative and real) analogues of von Neumann algebras - so called JW-algebras, i.e. real linear spaces of self adjoint opera.tors on a complex Hilbert space, which contain the identity operator 1. closed with respect to the Jordan (i.e. symmetrised) product INTRODUCTION 2 x 0 y = ~(Xy + yx) and closed in the weak operator topology. The structure of these algebras has happened to be close to the struc ture of von Neumann algebras and it was possible to apply ideas and meth ods similar to von Neumann algebras theory in the study of JW-algebras | ||
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Datensatz im Suchindex
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| author | Ayupov, Shavkat A. 1952- |
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| dewey-ones | 515 - Analysis |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-94-015-8605-4 |
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| id | DE-604.BV042424073 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:14Z |
| institution | BVB |
| isbn | 9789401586054 9789048148912 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027859490 |
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| spelling | Ayupov, Shavkat A. 1952- Verfasser (DE-588)124385672 aut Jordan, Real and Lie Structures in Operator Algebras by Shavkat Ayupov, Abdugafur Rakhimov, Shukhrat Usmanov Dordrecht Springer Netherlands 1997 1 Online-Ressource (IX, 230 p) txt rdacontent c rdamedia cr rdacarrier Mathematics and Its Applications 418 The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and investigation of general W* -algebras can be reduced to the case of factors. Therefore the theory of factors is one of the main tools in the structure theory of von Neumann algebras. In the middle of sixtieth Topping [To 1] and Stormer [S 2] have ini tiated the study of Jordan (non associative and real) analogues of von Neumann algebras - so called JW-algebras, i.e. real linear spaces of self adjoint opera.tors on a complex Hilbert space, which contain the identity operator 1. closed with respect to the Jordan (i.e. symmetrised) product INTRODUCTION 2 x 0 y = ~(Xy + yx) and closed in the weak operator topology. The structure of these algebras has happened to be close to the struc ture of von Neumann algebras and it was possible to apply ideas and meth ods similar to von Neumann algebras theory in the study of JW-algebras Mathematics Algebra Functional analysis Operator theory Functional Analysis Operator Theory Non-associative Rings and Algebras Associative Rings and Algebras Applications of Mathematics Mathematik Rachimov, Abdugafur A. Sonstige (DE-588)1158414048 oth Usmanov, Šuchrat M. Sonstige oth https://doi.org/10.1007/978-94-015-8605-4 Verlag Volltext |
| spellingShingle | Ayupov, Shavkat A. 1952- Jordan, Real and Lie Structures in Operator Algebras Mathematics Algebra Functional analysis Operator theory Functional Analysis Operator Theory Non-associative Rings and Algebras Associative Rings and Algebras Applications of Mathematics Mathematik |
| title | Jordan, Real and Lie Structures in Operator Algebras |
| title_auth | Jordan, Real and Lie Structures in Operator Algebras |
| title_exact_search | Jordan, Real and Lie Structures in Operator Algebras |
| title_full | Jordan, Real and Lie Structures in Operator Algebras by Shavkat Ayupov, Abdugafur Rakhimov, Shukhrat Usmanov |
| title_fullStr | Jordan, Real and Lie Structures in Operator Algebras by Shavkat Ayupov, Abdugafur Rakhimov, Shukhrat Usmanov |
| title_full_unstemmed | Jordan, Real and Lie Structures in Operator Algebras by Shavkat Ayupov, Abdugafur Rakhimov, Shukhrat Usmanov |
| title_short | Jordan, Real and Lie Structures in Operator Algebras |
| title_sort | jordan real and lie structures in operator algebras |
| topic | Mathematics Algebra Functional analysis Operator theory Functional Analysis Operator Theory Non-associative Rings and Algebras Associative Rings and Algebras Applications of Mathematics Mathematik |
| topic_facet | Mathematics Algebra Functional analysis Operator theory Functional Analysis Operator Theory Non-associative Rings and Algebras Associative Rings and Algebras Applications of Mathematics Mathematik |
| url | https://doi.org/10.1007/978-94-015-8605-4 |
| work_keys_str_mv | AT ayupovshavkata jordanrealandliestructuresinoperatoralgebras AT rachimovabdugafura jordanrealandliestructuresinoperatoralgebras AT usmanovsuchratm jordanrealandliestructuresinoperatoralgebras |