L1-Algebras and Segal Algebras
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Hans Reiter Mathematisch Instituut der Rijksuniversiteit De Uithof, Utrecht/Nederland
L1-Algebras and Segal Algebras
Springer-Verlag Berlin· Heidelberg· New York 1971
Lecture Notes in Mathematics A collection of informal reports and seminars Edited by A. Dold, Heidelberg and B. Eckmann, Zurich
231
Hans Reiter Mathematisch Instituut der Rijksuniversiteit De Uithof, Utrecht/Nederland
L1-Algebras and Segal Algebras
Springer-Verlag Berlin· Heidelberg· New York 1971
AMS Subject Classifications (1970): 43A20, 43A25, 43A45
ISBN 3-540-05651-3 Springer-Verlag Berlin' Heidelberg· New York ISBN 0-387-05651-3 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 1971. Library of Congress Catalog Card Number 76-178758. Printed in Germany.
Offsetdruck: Julius Beltz, Hemsbach/Bergstr.
PREFACE
L1-algebras of locally compact groups have been studied for many years. The systematic study of Segal algebras - which are a generalization of L1-algebras - was begun only a few years ago, for locally compact abelian groups. It is the purpose of these notes to study Segal algebras for general locally compact groups and to discuss also some new results for L1-algebras. There are many problems here for further research, and it is hoped that the reader will be able to continue where the author had to stop. The lectures of which these notes are the outcome were delivered at the Universities of Heidelberg, Nancy and Utrecht in 1969 and 1970. I wish to express here my cordial thanks to Professors H. Leptin (Heidelberg) and P. Eymard (Nancy) for their invitations and, especially, to my friends and colleagues in Utrecht who have made my long stay in the Netherlands so pleasant. Thanks are also due to Professor B. Eckmann of the Eidgenossische Technische Hochschule, Zurich, and to Springer-Verlag for making publication of these lectures possible. Dr. W. Beiglbock (Heidelberg), Mr. J.-P. Pier (Nancy) and Mr. M. Riemersma (Utrecht) have kindly provided me with their notes of the
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original lectures; Mr. Riemersma has also examined the manuscript itself and has contributed much helpful criticism. Last but not least, Miss W. Jenner (Utrecht) has typed the whole manuscript with the utmost care. My thanks go to each and all of them.
H.R.
1971
Mathematisch Instituut der Rijksuniversiteit De Uithof, Budapestlaan UTRECHT, The Netherlands
Address from 1 September 1971: Mathematisches Institut der Universitat, Strudlhofgasse 4 A 1090
VIENNA, Austria
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