NORTH-HOLLAND MATHEMATICS STUDIES 90 Notas de Matematica (94) Editor: Leopoldo Nachbin Centro Brasileiro de Pesquisas Fisicas and University of Rochester Functional Analysis: Surveys and Recent Results I11 Proceedings of the Conference on Functional Analysis Paderborn, Germany, 24-29 May, 1983 Edited by KLAUS-DIETER BIERSTEDT and BENNO FUCHSSTEINER University of Paderborn, Germany 1984 - NORTH-HOLLAND - AMSTERDAM NEW YORK OXFORD Elsevier Science Publishers B.V., I984 All rights reserved. Nop art of this publication may be reproduced, stored in a retrievalsystem, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the copyright owner. ISBN: 0 444 86866 6 Publishers: ELSEVIER SCIENCE PUBLISHERS B.V. P.O. BOX 1991 1000 BZ AMSTERDAM THE NETHERLANDS Sole distributors for the U.S.A . and Canada: ELSEVIER SCIENCE PUBLISHING COMPANY, INC. 52 VANDERBILT AVENUE NEW YORK, N.Y. 10017 Library of Congress Cataloging in Pubiicatioa Data Conference on Functional Analysis (3rd : 1983 : Paderborn, Germany Functional analysis ; surveys and recent results 111. (Notas de matedtica ; 94) (North-Holland mathematics studies ; 90) 1. Functional analysis--Congresses. I. Bierstedt, Klaus-Dieter. 11. Fwhssteiner, Benno. 111. Series: Notas de matedtica (Amsterdam, Netherlands) ; 94. Series: North-Holland mathematics studies ; 90. IV. gn319.C66 1983 515.7 84-1515 ISBN 0-444-86866-6 ) (U.S. PRINTED IN THE NETHERLANDS V PREFACE The First and Second Conferences on Functional Analysis at the University of Paderborn had been held in November 1976 and February 1979; their Proceedings were published (in 1977 and 1980) as volumes 27 (Notas de Matematica 63) and 38 (Notas de Matematica 68) of the North-Holland Mathematics Studies series, respectively. The Third Paderborn Conference on Functional Analysis took place from May 24 to May 29, 1983 (i. e., it was one day longer than the previous meetings). Organizers and editors of this volume, which contains the Proceedings of the conference, . were again K.-0. Bierstedt and B. Fuchssteiner - Many of the invited lecturers of the first two meetings also attended the 1983 conference; some of them gave short lectures, and others served as chairmen of the sessions. At the 1983 Paderborn Conference, there were 17 invited lectures (of 50 or 75 minutes each) on topics of current active research in functional analysis, operator theory, and related areas. Again, in accordance with the aim of this series of meetings, most of the speakers of the invited lectures first presented a survey of the theory, some motivation and background information in the first part of their talk before proceeding to recent contributions and new results. Since this conference was one day longer than those of 1977 and 1980, it was also possible to include 8 short lectures (of 25 minutes each), and four articles in this book were contributed from this part of the participants. - The joint paper of H. Goldmann, 6. Kram and 0. Vogt is based on discussions during the meeting, and for its origins see the remark at the end of (3.1) in Kramm's article. Further- more, one article was submitted by L. A. Moraes, a participant of the conference. As a glance at the table of contents shows, the 22 articles in this volume deal with many different aspects of functional analysis and its applications, ranging from Banach space theory and the theory of (nuclear) FrGchet spaces to e.g. positive operators, automatic continuity, C* - and von Neumann algebras, function algebras, distribution theory and convolution operators. vi Preface At the time when the manuscripts for this Proceedings volume kept arriving at Paderborn, we received the sad news of 6. Kramm's tragic death on October 11, 1983. All the participants of the conference will remember Bruno Kramm as an active and very energetic mathematician, full of interesting ideas. We all deeply regret this great loss. The original plans for Kramm's survey article in these Proceedings included 8 chapters of which, due to his severe illness this summer and fall, only 4 could actually be finished. In the preparation of his contribution (and of the manus- cript in this volume), Kramm was helped by his student, Goldmann. In fact, as H. time went on and Kramm's health situation became critical, Goldmann was, more and more, on his own, turning the notes into the final version of the paper. Of course, the present article "Nuclearity and function algebras - a survey -I' by Bruno Kramm is not really what Kramm had in mind when he started writing it and what the editors had hoped to receive. E.g., it does not contain an introduction and breaks off at the end of chapter 4. However, in its organization and in the inclusion of problems and interesting remarks, it clearly reflects Kramm's spirit and some of his research on the borderlines between functional analysis, several complex variables and function algebras. So we decided to include the manuscript in these Proceedings. It remains to thank once more all those who participated in the meeting for their interest and the stimulating discussions, above all the speakers and the chairmen of the sessions. We thank all the contributors for the preparation of their manus- cripts in time for the publication (the deadline was, more or less, September 30, 1983, but the last paper actually arrived at Paderborn in late November). We thank the analysis group of Paderborn for their help in organizing the meeting and in proofreading the manuscripts; we mention J. Cioranescu, 6. Ernst. R. Hollstein and, above all, Wolfgang Lusky in this connection. Ms. 6. Duddeck did an excellent job with the typing of two manuscripts (and the first pages of the book) as well as with the correction of many misprints. Finally, we would like to thank "Stiftung Volkswagenwerk" for providing the funds for the conference, Paderborn for all the support, the Universitat-Gesamthochschule editor of Notas de MatemStica, Leopoldo Nachbin, and the publisher for including this volume in their series. K. D. Bierstedt 6. Fuchssteiner Editors' address: K.-D. Bierstedt, Fuchssteiner, FB 17, Mathematik, B. Universitat-Gesamthochschule- Paderborn, Postfach 16 21, 0-4790 Paderborn, Germany vi i SCHEDULE OF LECTURES Wednesday, May 25, 1983: Morning Session 9.00 Opening Session Chairman: J. Schmets (Lie'ge) 9.30 - 10.45 H. G. Dales (Leeds), Automatic continuity of homomorphisms from C*-a1 gebras Chairman: S. 0. Chatterji (Lausanne) - 11.15 12.30 E. G. F. Thomas (Groningen), The theorem of Bochner-Schwartz- Godement for generalized Gelfand pairs Afternoon Session Chairman: G. Ma1 tese (Munster) 2.30 - 3.20 H. H. Schaefer (Tubingen), Positive bilinear forms and the Radon- N ik odym theorem - 3.30 4.20 R. Nagel (Tubingen), What can positivity do for stability? Chairman: E. Albrecht (Saarbrucken) 4.40 - 5.55 K. B. Laursen (Copenhagen), Commutative homomorphisms from C*-a1 gebras Thursday, May 26, 1983: Morning Session Chairman: T. Terzioglu (Ankara /Wuppertal) 9.00 - 10.15 0. Vogt (Wuppertal), Recent results on continuous linear maps between FrEchet spaces viii Schedule of Lectures Chairman: W. Kaballo (Dortmund) 10.25 11.15 R. Meise (Dusseldorf), Power series spaces of infinite type in discrete weighted interpolation theory and as kernels of convolution operators 12.05 12.30 V. Aurich (Munchen), Bounded holomorphic embeddings of the unit disk into Banach spaces Afternoon Session Chairman: H. G. Tillmann (Munster) 2.30 - 3.45 H. P. Lotz (Urbana /Tubingen), Uniform convergence of operators in Lm and similar spaces 3.55 - 4.20 R. M. Aron (Dublin), Infinite dimensional polydisc algebras Chairman: M. Neumann (Essen) 4.40 - 5.30 L. Weis (Kaiserslautern), Decompositions of positive operators and some of their applications 5.40 - 6.05 P. PPrez Carreras (Valencia), Preservation of barreledness proper- ties in tensor products Friday, May 27, 1983: Morning Session Chairman: H. Konig (Kiel) 9.00 - 10.15 P. Wojtaszczyk (Warszawa), The Banach space H, Chairman: 6. Gramsch (Mainz) 10.45 - 12.00 A. PeTczyiiski (Warszawa), Critical exponents - 12.10 12.35 C. Schutt (Kiel), On the positive. projection constant Afternoon Session Chairman: H. J. Petzsche (Dusseldorf) 2.30 - 3.45 B. Kramm (Bayreuth), Nuclearity and function algebras C hair man : M. Wol ff (Tubi ngen ) 4.05 - 4.55 K. Donner (Munchen), Extension of operators and approximation by linear operators c z Schedule of Lectures ix 7 1 5.05 - 5.30 H. v. Weizsacker (Kaiserslautern), Orthogonal kernels Saturday, May 28, 1983: Morning Session Chairman: G. Hegerfeldt (Gottingen) 9.00 - 9.50 G. Wittstock (Saarbrucken), Matrix convex analysis on operator a1 gebras 10.00 - 10.25 D. Petz (Budapest), Ergodic theorems in von Neumann algebras Chairman: K. Floret (Kiel) 10.55 - 12.10 P. Dierolf (Trier), Multiplication operators between spaces of distributions 12.20 - 12.45 R. Mennicken (Regensburg), An elementary proof of a theorem of Kel dyS Afternoon Session Chairman: A. Cost6 (Dakar/Caen) 2.45 - 3.35 H. Jarchow (Zurich), Hilbertisable topologies on Banach spaces Chairman: W. Lusky (Paderborn) 4.00 - 4.50 C. Stegall (Linz), A class of topological spaces and differentiation of functions on Banach spaces 5.00 - 5.25 W. Ruess (Essen), Geometry of operator spaces. X LIST OF PARTICIPANTS Albrecht, Saarbrucken E. Marschall, Munster E. R. M. Aron, Dublin (Ireland) R. Meise, Dusseldorf V. Aurich, Munchen R. Mennicken, Regensburg K. 0. Bierstedt, Paderborn M. Moller, Regensburg J. Bonet, Valencia (Spain) L. A. de Moraes, Rio de Janeiro (Brazil) J. Boos, Hagen R. Nagel, Tubingen A. S. Chatterji, Lausanne (Switzerland) M. Neumann, Essen I. Cioranescu, Paderborn G. Niestegge, Munster A. Cost&, Dakar (Senegal) / Caen (France) A. PeTczyhski, Warszawa (Poland) J. Cu&llar, Mainz P. Perez, Valencia (Spain) H. G. Dales, Leeds (England) Petz, Budapest (Hungary) 0. A. Defant, Oldenburg H. J. Petzsche, Dusseldorf P. Dierolf, Trier C. Portenier, Marburg K. Donner, Munchen K. Reiher, Paderborn B. Ernst, Paderborn F. Reuter, Marburg K. Floret, Oldenburg W. Ruess, Essen B. Fuchssteiner, Paderborn H. Schaefer, Tubingen H. P. Furland, Dortmund J. Schmets, Liege (Belgium) J. Glaser, Dortmund K. 0. Schmidt, Mannheim H. Goldmann, Bayreuth M. Schottenloher, Munchen 6. Gramsch, Mainz C. Schutt, Kiel S. Hansen, Paderborn T. Schunk, Dortmund G. Hegerfeldt, Gottingen K. Schwerdtfeger, Dusseldorf R. Hollstein, Paderborn C. Stegall, Linz (Austria) G. Janssen , Braunschwei g T. Terzioglu, Ankara (Turkey) / Wuppertal H. Jarchow, Zurich (Switzerland) H. G. Tillmann, Munster W. Kaballo, Dortmund E. G. F. Thomas, Groningen (Netherlands) H. Konig, Kiel K. Ulrich, Clausthal B. Kramm, Bayreuth 0. Vogt, Wuppertal M. Langenbruch, Munster R. Wagner, Paderborn C. Larisch, Munster L. Weis, Kaiserslautern K. B. Laursen, Copenhagen (Denmark) H. v. Weizsacker, Kaiserslautern T. Leiger, Tartu (USSR) / Hagen 0. Werner, Berlin E.-0. Liebetrau, Oldenburg G. Wittstock, Saarbrucken H. P. Lotz, Urbana (USA) / Tubingen P. Wojtaszczyk, Warszawa (Poland) W. Lusky, Paderborn M. Wolff, Tubingen G. Maltese, Munster J. Wolter, Bayreuth A. Marquina, Valencia (Spain) xi LIST OF CONTRIBUTORS H. G. Dales, School of Mathematics, University of Leeds, Leeds, LS2 9JT, England P. Dierolf, Fachbereich IV, Mathematik, Universitat Trier, Postfach 38 25, D-5500 Trier, Germany K. Donner, Lehrstuhl fur Mathematik, Universitat Passau, Postfach 25 40, D-8390 Passau, Germany H. Goldmann and 6. Kramm, Mathematisches Institut, Universitat Bayreuth, Postfach 30 08, 5-8580 Bayreuth, Germany H. Jarchow, Institut fur Angewandte Mathematik, Universitat Zurich, RamistraRe 74, CH-8001 Zurich, Switzerland K. B. Laursen, Mathematics Institute, University of Copenhagen, DK-2100 Copenhagen, Denmark H. P. Lotz, Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A. R. Meise, Mathematisches Institut, Universitat DUsseldorf, Universitatsstr. 1, D-4000 Dusseldorf, Germany R. Mennicken and M. Moller, Naturwissenschaftliche Fakultat I, Mathematik, Universi tat Regensburg, Universitatsstr. 31, D-8400 Regensburg, Germany L. Moraes, Instituto de Matemstica, Universidade Federal do Rio de Janeiro, A. C.P. 68530, 21944 Rio de Janeiro, Brazil R. Nagel, Mathematisches Institut, Universitat Tubingen, Auf der Morgenstelle 10, D-7400 Tubingen 1, Germany D. Petz, Mathematical Institute, Hungarian Academy of Sciences, Budapest H-1395, P.D.B. 428, Hungary W. Ruess, Fachbereich Mathematik, Universitat Essen, Universitatsstr. 3, D-4300 Essen Germany H. H. Schaefer, Mathematisches Institut, Universitat Tubingen, Auf der Morgenstelle 10, D-7400 Tubingen 1, Germany C. Schutt, Mathematisches Institut, Christian-Albrechts-Universitat, Olshausenstr. 40 - 60, D-2300 Kiel 1, Germany C. Stegall, Mathematisches Institut, Johannes Kepler-Universitat, A-4540 Linz, Austria E. G. F. Thomas, Department of Mathematics, Groningen University, P.O. 800, Box NL-9700 AV Groningen, The Netherlands xii List qf Contributors D. Vogt, Fachbereich Mathematik, Universitat-Gesamthochschule-Wuppertal, GauBstr. 20, D-5600 Wuppertal 1, Germany L, W. Weiss, Fachbereich Mathematik, Universitat Kaiserslautern, Postfach 30 49, D-6750 Kaiserslautern, Germany G. Wittstock, Fachbereich Mathematik, Universitat des Saarlandes, D-6600 Saarbrkken , Germany P. Wojtaszczyk, Institute of Mathematics, Polish Academy of Sciences, ul. Sniadeckich 8, 00-950 Warszawa, Poland