Non-Associative Normed Algebras: Volume 2, Representation Theory and the Zel'manov Approach
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| Title: | Non-Associative Normed Algebras: Volume 2, Representation Theory and the Zel'manov Approach |
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| Description: | This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB•-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C•-algebras and non-commutative JB•-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography. |
| Authors: | Miguel Cabrera García, Ángel Rodríguez Palacios |
| Resource Type: | eBook. |
| Subjects: | Algebra, Banach algebras |
| Categories: | MATHEMATICS / Algebra / Abstract |
| Database: | eBook Collection (EBSCOhost) |
| Abstract: | This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB•-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C•-algebras and non-commutative JB•-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography. |
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| ISBN: | 9781107043114 9781108631433 |
