Table Of ContentNORTH-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
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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
