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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,...

This book grew out of an introductory course that I was invited to teach on a number of occasions to senior and graduate level students at the University of Kid. I have cherished these opportunities in part because I was never required to conduct examinations or give grades. For the students, however, my good fortune presented special problems that induced my sympathy: in addition to having to contend with a foreign language, they would eventually have to confront an examiner with his own ideas about what they should have learned. Although I always left a copy of my lecture notes with this...

K -Theory has revolutionized the study of operator algebras in the last few years. As the primary component of the subject of "noncommutative topol ogy," K -theory has opened vast new vistas within the structure theory of C* algebras, as well as leading to profound and unexpected applications of opera tor algebras to problems in geometry and topology. As a result, many topolo gists and operator algebraists have feverishly begun trying to learn each others' subjects, and it appears certain that these two branches of mathematics have become deeply and permanently intertwined. Despite the fact...

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,...

K-theory has helped convert the theory of operator algebras from a simple branch of functional analysis to a subject with broad applicability throughout mathematics, especially in geometry and topology, and many mathematicians of diverse backgrounds must learn the essential parts of the theory. This book is the only comprehensive treatment of K-theory for operator algebras, and is intended to help students, non specialists, and specialists learn the subject. This first paperback printing has been revised and expanded and contains an updated reference list. This book develops K-theory, the...