Locally Convex Spaces
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cally Convex Spaces by Dr. phil. Hans Jarchow Professor at the University of Zürich
B. G. Teubner Stuttgart 1981
Prof. Dr. phi!. Hans Jarchow Born 1941 in Bremerhaven. Studies in Hamburg and Zürich from 1960 to 1966. Received diploma in 1966 and Ph.D. in 1967from the University ofZürich. At the University of Zürich, lecturer from 1969 to 1970, assistant professor from 1970 to 1979, and associate professor beginning in 1979. Visiting professor at the University of Maryland from 1974 to 1975.
CIP-Kurztitelaufnahme der Deutschen Bibliothek Jarchow, Hans: Locally convex spaces / by Hans Jarchow. Stuttgart : Teubner, 1981. (Mathematische Leitfaden) ISBN 978-3-322-90561-1 ISBN 978-3-322-90559-8 (eBook) DOI 10.1007/978-3-322-90559-8
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, reproductions by photocopying machine or similar means, and storage in data banks. Under § 54 ofthe Gerrnan Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount ofthe fee to be deterrnined by agreement with the publisher. © B. G. Teubner, Stuttgart 1981 Setting: Schmitt u. Köhler, Würzburg
Cover design: W. Koch, Sindelfingen
Ta Szazy
Preface The present book grew out of several courses which I have taught at the University of Zürich and at the University of Maryland during the past seven years. It is primarily intended to be a systematic text on locally convex spaces at the level of a student who has some familiarity with general topology and basic measure theory. However, since much of the material is of fairly recent origin and partly appears here for the first time in a book, and also since some well-known material has been given a not so well-known treatment, I hope that this book might prove useful even to more advanced readers. And in addition I hope that the selection ofmaterial marks a sufficient set-offfrom the treatments in e.g. N. Bourbaki [4], [5], R.E. Edwards [1], K. Floret-J. Wloka [1], H.G.Garnir-M.De Wilde-J.Schmets [1], AGrothendieck [13], H.Heuser [1], J. Horvath [1], J. L. Kelley-I. Namioka et al. [1], G. Köthe [7], [10], A P. RobertsonW.Robertson [1], W.Rudin [2], H.H.Schaefer [1], F.Treves [l],A Wilansky [1]. A few sentences should be said about the organization of the book. It consists of 21 chapters which are grouped into three parts. Each chapter splits into several sections. Chapters, sections, and the statements therein are enumerated in consecutive fashion. Cross references are usually k.m.n. meaning that reference is made to statement n of section m in chapter k. Inside of k.m (i.e. of seetion m in chapter k) reference is simply to n rather than to k.m.n. Definitions are not listed as separate statements, they are only distinguished from the text by using spaced type characters. The end of a proof is marked by •. Starting from Chapter 2, each chapter concludes with a reference section, intended to give
