Derived Functors in Functional Analysis
The text contains for the first time in book form the state of the art of homological methods in functional analysis like characterizations of the vanishing of the derived projective limit functor or the functors Ext1 (E, F) for Fréchet and more general s
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Jochen Wengenroth
Derived Functors in Functional Analysis
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Author Jochen Wengenroth FB IV - Mathematik Universit¨at Trier 54286 Trier, Germany E-mail: [email protected]
Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at http://dnb.ddb.de
Mathematics Subject Classification (2000): 46M18, 46M40, 46A03, 46A13, 46E10, 46F05, 46N20, 18E25, 35E20 ISSN 0075-8434 ISBN 3-540-00236-7 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. Springer-Verlag Berlin Heidelberg New York a member of BertelsmannSpringer Science + Business Media GmbH http://www.springer.de c Springer-Verlag Berlin Heidelberg 2003 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specif ic statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera-ready TEX output by the author SPIN: 10825800
41/3142/du-543210 - Printed on acid-free paper
Acknowledgements
It is a great pleasure to thank my friend Leonhard Frerick who was always willing and able to discuss my problems and often helped to solve them. I am indebted to Susanne Dierolf who has been a constant source of help and encouragement for a long time. Professors K.-D. Bierstedt, J. Bonet, and D. Vogt kindly contributed several valuable suggestions. The typing of the manuscript (using AMS-LATEX) was mainly done by Lisa Schmitt. I thank her very much. The diagrams are produced using the package “Commutative Diagrams in TEX” of Paul Taylor. The bibliography was produced with BibTEX using the database MathSciNet of the American Mathematical Reviews.
Table of Contents
1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
2
Notions from homological algebra . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1 Derived Functors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 The category of locally convex spaces . . . . . . . . . . . . . . . . . . . . . 13
3
The projective limit functor for count
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