Non-Associative Normed Algebras

The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.

Miguel Cabrera García (Author), Ángel Rodríguez Palacios (Author)

9781107043060, Cambridge University Press

Hardback, published 31 July 2014

733 pages, 3 b/w illus. 20 exercises
24 x 15.9 x 4.4 cm, 1.23 kg

'I dare say that this book is the first detailed treatise whose primary goal is the study of normed nonassociative algebras. The two authors are recognized experts in this topic, which combines functional analysis, geometry of Banach spaces and what could be called structure theory of algebras which are nearly associative.' Antonio Fernández López, zbMATH (www.zbmath.org)

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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

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.

Subject Areas: Algebra [PBF], Mathematics [PB]