Lectures on Operator Algebras
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Lectures on Operator Algebras
Springer-Verlag Berlin · Heidelberg · NewYork 1972
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AMS Subject Classifications (1970): 18H15, 22D15, 22D20, 22D25, 22D30, 22D35, 43A05, 43AlO, 46L05, 46L10, 46L25, 46M05, 47B20 ----- ------ --- ------
ISBN 3-540-05729-3 Springer-Verlag Berlin - Heidelberg - New York ISBN 0-387-05729-3 Springer-Verlag New York : Heidelberg· Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin' Heidelberg 1972. Library of Congress Catalog Card Number 72-189460. Printed in Germany.
Offsetdruck: Julius Beltz, HemsbachlBergstt.
ACKNOWLEDGEMENTS
The special year in the Theory of Rings and Operator Algebras was the third program of a similar kind held at Tulane University, following one in the Theory of C*-Algebras and one in Category Theory.
These programs were made possible solely through a grant
from the Ford Foundation.
We wish to express our sincere gratitude
to the Ford Foundation for its generous support and cooperation. A few participants were supported by other agencies:
Hans H.
Storrer held a fellowship of the Schweizerischer Nationalfonds zur Foderung der Wissenschaftlichen Forschung while he spent the year at Tulane University.
Silviu Teleman was able to spend several
months at Tulane University, thanks to the exchange program between the National Academy of Sciences of the U. S. A. and the Academy of Sciences of the Socialist Republic of Rumania. Tulane University provided the facilities for the program and administered the grant. Most of these notes were typed efficiently and patiently by the secretarial staff of the Mathematics Department of Tulane University. Karl Heinrich Hofmann
DEDICATION
This volume of lecture notes about Operators on Hilbert space and von Neumann A1gebras is dedicated to the memory of
DAVID M. TOPPING
who died on October 21, 1970, after a brief illness.
His interest
in the field inspired this series of lectures, and he was one of the organizers of the program.
His presence and activity at Tulane
attracted many of the visitors who participated in the program and hoped to work with him and benefit from his rich experience and his numerous contributions to the field.
The mathematical cOllllllunity
has lost a fine mathematician and colleague.
PREFACE
From September 1970 through May 1971 Tulane University organized a special year long program in the theory of non-collUllutative rings and operator algebras.
Visitors from various institutions of the
U.S.A. and abroad contributed series of lectures in which they covered recent advances in their ow
