Non-Associative Normed Algebras 2 Volume Hardback Set
Non-Associative Normed Algebras 2 Volume Hardback Set
$293.00
USDThis first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. The 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 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. 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.
- Brings together research previously scattered across many different papers and books
- Authors are both leading experts in the field
- Unique resource for students and researchers in the field
Reviews & endorsements
'Just as the first volume of this monograph, the second volume under review here deserves the attention of nearly everybody interested in functional analysis and its applications, as well as of many people with an interest in several complex variables or in the theory of Lie groups. The authors skillfully present in a self-contained and well-motivated manner such basic topics as differential calculus on Banach spaces, infinitedimensional holomorphy, vector fields and their flows, Banach-Lie group structure on the holomorphic automorphisms of a bounded domain in a Banach space, or joint spectral radius in Banach algebras. This book is a really great achievement on the part of the authors and studying it or even parts of it will be both pleasant and profitable to the reader.' Daniel Beltita, Mathematical Reviews
Product details
May 2018Multiple copy pack
9781108679077
1494 pages
241 × 165 × 85 mm
2.44kg
Temporarily unavailable - available from TBC
Table of Contents
- Volume 1: 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. Volume 2: Preface
- 5. Non-commutative JBW*-algebras, JB*-triples revisited, and a unit-free Vidav–Palmer type non-associative theorem
- 6. Representation theory for non-commutative JB*-algebras and alternative C*-algebras
- 7. Zel'manov approach
- 8. Selected topics in the theory of non-associative normed algebras
- Reference – Papers
- References – Books
- Symbol index for Volume 2
- Subject index for Volume 2
- Symbol index for Volume 1
- Subject index for Volume 1.
