The Vidav-Palmer and Gelfand-Naimark theorems
著者
書誌事項
The Vidav-Palmer and Gelfand-Naimark theorems
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 154 . Non-associative normed algebras ; v. 1）
Cambridge University Press, 2014
- : hardback
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注記
Includes bibliographical references (p. [671]-703) and indexes
内容説明・目次
内容説明
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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 first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand-Naimark and Vidav-Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography.
目次
- Preface
- 1. Foundations
- 2. Beginning the proof of the non-associative Vidav-Palmer theorem
- 3. Concluding the proof of the non-associative Vidav-Palmer theorem
- 4. Jordan spectral theory
- References
- Symbol index
- Subject index.
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