Functional Analysis Proceedings of the Seminar at the University of
The papers in this volume yield a variety of powerful tools for penetrating the structure of Banach spaces, including the following topics: the structure of Baire-class one functions with Banach space applications, operator extension problems, the structu
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Lecture Notes in Mathematics Editors: A. Dold, Heidelberg B. Eckmann, Zurich F. Takens, Groningen
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E. Odell
H. Rosenthal (Eds.)
Functional Analysis Proceedings of the Seminar at the University of Texas at Austin 1987-89
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Barcelona Budapest
Editors Edward E. Odwell, jr. Haskell P. Rosenthal Department of Mathematics The University of Texas at Austin Austin, TX 78712, USA
Mathematics Subject Classification (1980): Primary: 46B20, 46A55 Secondary: 42A61, 43A99, 46H99, 47D99, 54F60
ISBN 3-540-54206-X Springer-Verlag Berlin Heidelberg New York ISBN 0-387-54206-X Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9,1965, in its current version, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1991 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210 - Printed on acid-free paper
Longhorn Notes
Preface
This is the sixth annual proceedings of our Functional Analysis Seminar at The University of Texas, and the second one to be published in the Springer-Verlag Lecture Notes. All the articles that appear are based on talks given in the seminar during the years 1987-89. We thank the participants for their effort in communicating mathematical ideas in both spoken and written form. We again wish to express our deep appreciation to Margaret Combs for her expert craftsmanship and considerable patience in typesetting this issue. Thanks are also due to The University of Texas for supporting the publication of the Longhorn Notes. Ted Odell Haskell Rosenthal August 1990
TABLE OF CONTENTS
Page 1. On certain classes of Baire-I functions with applications to Banach space theory by R. Haydon, E. Odell and H. Rosenthal
1
2. Normed spaces with a weak-Gordon-Lewis property by K. Ball
36
3. On the geometry of the Banach-Mazur compactum by S.J. Szarek
48
4. Some remarks about the space of measures with uniformly bounded partial sums and Banach-Mazur distances between some spaces of polynomials by P. Wojtaszczyk
60
5. Operators which factor through Banach lattices not containing Co by N. Ghoussoub and W.B. Johnson
68
6. Remarks on Talagrand's deviation inequality for Rademacher functions by W.B. Johnson and G. Schechtman
72
7. A Global Approach to Certain Operator Extension Problems by M. Zippin
78
8. Weakly null sequences with upper t'p-estimates by H. Knaust and E. Odell
85
9. On tensor products of operators from LP to Lq by H.P. Rosenthal and S.J. Szarek
108
10. Limited Sets in Injective
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