Non-Associative Normed Algebras

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Miguel Cabrera García (Universidad de Granada) Ángel Rodríguez Palacios (Universidad de Granada)

Non-Associative Normed Algebras

Miguel Cabrera García (Universidad de Granada), Ángel Rodríguez Palacios (Universidad de Granada)

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English

Cambridge University Press
12 April 2018

Algebra; Functional analysis & transforms; Algebraic topology

Series: Encyclopedia of Mathematics and its Applications

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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

By: Miguel Cabrera García (Universidad de Granada), Ángel Rodríguez Palacios (Universidad de Granada)
Imprint: Cambridge University Press
Country of Publication: United Kingdom
Volume: Volume 2
Dimensions: Height: 240mm, Width: 160mm, Spine: 46mm
Weight: 1.280kg
ISBN: 9781107043114
ISBN 10: 1107043115
Series: Encyclopedia of Mathematics and its Applications
Pages: 754
Publication Date: 12 April 2018
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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; Bibliography of Volume 1; Additional bibliography to Volume 2; Symbol index for Volume 1; Subject index for Volume 1; Symbol index for Volume 2; Subject index for Volume 2.

Miguel Cabrera García 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. Ángel Rodríguez 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.

Reviews for Non-Associative Normed Algebras

'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 '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