Non Associative Normed Algebras Volume 2 Representation Theory and the Zel manov Approach 1st Edition Miguel Cabrera García 9781107337817

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Product details:

• ISBN 13: 9781107337817
• Author: Miguel Cabrera García

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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.

Table of contents:

5 – Non-commutative JBW ∗-algebras, JB ∗-triples revisited, and a unit-free Vidav–Palmer type non-

6 – Representation theory for non-commutative JB ∗-algebras and alternative C ∗-algebraspp 347-436

7 – Zel’manov approachpp 437-476

8 – Selected topics in the theory of non-associative normed algebras

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