Jordan, Real and Lie Structures in Operator Algebras by Sh. AyupovJordan, Real and Lie Structures in Operator Algebras by Sh. Ayupov

Jordan, Real and Lie Structures in Operator Algebras

bySh. Ayupov, Abdugafur Rakhimov, Shukhrat Usmanov

Paperback | December 15, 2010

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This book develops a new approach to the study of infinite-dimensional Jordan and Lie algebras and real associative *-algebras of operators on a Hilbert space. All these algebras are canonically generated by involutive antiautomorphisms of von Neumann algebras. The first purpose of the book is to study the deep structure theory for Jordan operator algebras similar to (complex) von Neumann algebras theory, such as type classification, traces, conjugacy of automorphisms and antiautomorphisms, injectivity, amenability, and semidiscreteness. The second aim is to investigate pure algebraic problems concerning Jordan and Lie structure in prime and simple rings with involution in the frame work of operator algebras. These pure algebraic results give additional information on properties of single operators on a Hilbert space. Audience: This volume will be of interest to postgraduate students and specialists in the field of operator algebras, and algebraists whose work involves nonassociative and infinite-dimensional rings.
Title:Jordan, Real and Lie Structures in Operator AlgebrasFormat:PaperbackDimensions:239 pages, 9.25 × 6.1 × 0 inPublished:December 15, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:904814891X

ISBN - 13:9789048148912

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Table of Contents

Introduction. Preliminaries. 1. Jordan Operator Algebras. 2. Real Structure in W*-Algebras. 3. Lie Structure in Operator Algebras. References. Index.