Theory of Operator Algebras I / Edition 1

by M. Takesaki

Overview

Since its inception by von Neumann 70 years ago, the theory of operator algebras has become a rapidly developing area of importance for the understanding of many areas of mathematics and theoretical physics. Accessible to the non-specialist, this first part of a three volume treatise provides a clear, carefully written survey that emphasizes the theory's analytical and topological aspects.

The book's unifying theme is the Banach space duality for operator algebras. This allows the reader to recognize the affinity between operator algebras and measure theory on locally compact spaces. Very technical sections are clearly labeled and there are extensive comments by the author, a good historical background and excercises.

This book is part of the subseries of the EMS on Operator Algebras and Non-Commutative Geometry.

Product Details

ISBN-13:	9783540422488
Publisher:	Springer Berlin Heidelberg
Publication date:	12/18/2001
Series:	Encyclopaedia of Mathematical Sciences , #124
Edition description:	1st ed. 1979. 2nd printing 2001
Pages:	415
Product dimensions:	6.14(w) x 9.21(h) x 0.04(d)

Table of Contents

Fundaments of Banach Algebras and C*-Algebras.- Topologies and Density Theorems in Operator Algebras.- Conjugate Spaces.- Tensor Products of Operator Algebras and Direct Integrals.- Types of von Neumann Algebras and Traces.- Appendix: Polish Spaces and Standard Borel Spaces.

Editorial Reviews

"... These three bulky volumes [EMS 124, 125, 127], written by one of the most prominent researchers of the area, provide an introduction to this repidly developing theory. ... These books can be warmly recommended to every graduate student who wants to become acquainted with this exciting branch of matematics. Furthermore, they should be on the bookshelf of every researcher of the area." (László Kérchy, Acta Scientiarum Mathematicarum, Vol. 69, 2003)

From the Publisher