Non-Associative Normed Algebras: Volume 1, The Vidav–Palmer and Gelfand–Naimark Theorems

Miguel Cabrera García, Ángel Rodríguez Palacios

• Publisher: Cambridge University Press
• Year: 2014
• Print ISBN: 9781107043060
• eBook ISBN: 9781139990455
• Topic: Mathematics
• Subtopic: Abstract Algebra
• Index: Mathematics

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first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field.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

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Table of contents
• 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