The Vidav-Palmer and Gelfand-Naimark theorems
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Bibliographic Information
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
Available at / 38 libraries
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
: hardbackS||EMA||154200029525109
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
: hardback/C 1122080350927
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Note
Includes bibliographical references (p. [671]-703) and indexes
Description and Table of Contents
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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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 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.
Table of Contents
- 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.
by "Nielsen BookData"