Jordan, Real and Lie Structures in Operator Algebras

This title is printed to order. This book may have been self-published. If so, we cannot guarantee the quality of the content. In the main most books will have gone through the editing process however some may not. We therefore suggest that you be aware of this before ordering this book. If in doubt check either the author or publisher’s details as we are unable to accept any returns unless they are faulty. Please contact us if you have any questions.

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.