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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. 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.
Rezensionen / Stimmen
'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
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
Worked examples or Exercises
Maße
Höhe: 240 mm
Breite: 162 mm
Dicke: 89 mm
Gewicht
ISBN-13
978-1-108-67907-7 (9781108679077)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Miguel Cabrera Garcia is a Professor in the Department of Mathematical Analysis at the University of Granada, Spain. He is a leading expert in non-associative normed algebras and multiplication algebras, and has collaborated with outstanding mathematicians, including M. Bresar, W. S. Martindale III, and E. I. Zel'manov. Angel Rodriguez Palacios is a Professor in the Department of Mathematical Analysis at the University of Granada, Spain. He is regarded as the world leader in non-associative normed algebras, and has written more than 150 research papers on normed spaces and associative and non-associative normed algebras. Some of these papers have been written in collaboration with others, including C. H. Chu, H. G. Dales, W. Kaup, M. Neumann, A. M. Slin'ko, D. Yost, G. V. Wood, and E. I. Zel'manov.
Autor*in
Universidad de Granada
Universidad de Granada
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.
