Operator Algebras: Theory of C*-Algebras and von Neumann Algebras (Encyclopaedia of Mathematical Sciences Book 122)

This book is the most comprehensive treatment available of the general theory of C\*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, classification of injective factors, K-theory, finiteness, stable rank, and quasidiagonality. The presentation concentrates on carefully and precisely explaining the main features of each part of the theory of operator algebras; most important arguments are at least outlined, and many are presented in full detail, so the volume is much more than a mere survey. This volume attempts to give a comprehensive discussion of the theory of operator algebras (C*-algebras and von Neumann algebras. ) The volume is intended to serve two purposes: to record the standard theory in the Encyc- pedia of Mathematics, and to serve as an introduction and standard reference for the specialized volumes in the series on current research topics in the subject. Since there are already numerous excellent treatises on various aspects of thesubject,howdoesthisvolumemakeasigni?cantadditiontotheliterature, and how does it di?er from the other books in the subject? In short, why another book on operator algebras? The answer lies partly in the ?rst paragraph above. More importantly, no other single reference covers all or even almost all of the material in this volume. I have tried to cover all of the main aspects of “standard” or “clas- cal” operator algebra theory; the goal has been to be, well, encyclopedic. Of course, in a subject as vast as this one, authors must make highly subjective judgments as to what to include and what to omit, as well as what level of detail to include, and I have been guided as much by my own interests and prejudices as by the needs of the authors of the more specialized volumes. This Book Is The Most Comprehensive Treatment Available Of The General Theory Of C*-algebras And Von Neumann Algebras. Beginning With The Basics, The Theory Is Developed Through Such Topics As Tensor Products, Nuclearity And Exactness, Crossed Products, Classification Of Injective Factors, K-theory, Finiteness, Stable Rank, And Quasidiagonality.--book Jacket. I. Operators On Hilbert Space -- Ii. C*-algebras -- Iii. Von Neumann Algebras -- Iv. Further Structure -- V. K-theory And Finiteness. B. Blackadar. Includes Bibliographical References (pages 479-503) And Index. This book offers a comprehensive introduction to the general theory of C*-algebras and von Neumann algebras. Beginning with the basics, the theory is developed through such topics as tensor products, nuclearity and exactness, crossed products, K-theory, and quasidiagonality. The presentation carefully and precisely explains the main features of each part of the theory of operator algebras; most important arguments are at least outlined and many are presented in full detail. front-matter......Page 1 1Operators on Hilbert Space......Page 17 2C-Algebras......Page 66 3Von Neumann Algebras......Page 235 4Further Structure......Page 337 5K-Theory and Finiteness......Page 409 back-matter......Page 492