Tsirelson's Space With an Appendix by J. Baker, O. Slotterbeck and R
This monograph provides a structure theory for the increasingly important Banach space discovered by B.S. Tsirelson. The basic construction should be accessible to graduate students of functional analysis with a knowledge of the theory of Schauder bases,
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1363 Peter G. Casazza Thaddeus J. Shura
Tsirelson's Space With an Appendix by J. Baker, O. Siotterbeck and R. Aron
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Lecture Notes in Mathematics Edited by A. Dold and B. Eckmann
1363 Peter G. Casazza Thaddeus J. Shura
Tsirelson's Space With an Appendix by J. Baker, O. Siotterbeck and R. Aron
Springer-Verlag Berlin Heidelberg New York London Paris Tokyo
Authors
Peter G. Casazza Department of Mathematics, University of Missouri Columbia, MO 65211, USA Thaddeus J. Shura Kent State University, Salem Campus South Salem OH 44460, USA
Mathematics Subject Classification (1980): 46B20, 46B25 ISBN 3-540-50678-0 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-50678-0 Springer-Verlag New York Berlin Heidelberg
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© Springer-Verlag Berlin Heidelberg 1989 Printed in Germany Printing and binding: Druckhaus Beltz, Hemsbach/Bergstr. 2146/3140-543210
Dedication
We dedicate these notes to Professor R. C. James.
Preface
One of the historical concerns of the structure theory of Banach spaces has been whether there were any 'fundamental" spaces which embedded isomorphically in every infinite-dimensional Banach space.
". . . from the point of view of the theory of classical Banach spaces the
'nicest' subspace one could possibly hope to find in a general Banach space would be either Co
:s: p < (0). The feeling that this could be the case was based on the fact that all classical spaces do indeed contain a copy of Co or fp(l :s: p < (0). Also Orlicz spaces have this property or f p(l
despite the fact that . . . the definition of an Orlicz space is not a priori connected to any f p space or co." [55] The classical hope that Co or some f p always embeds in a general Banach space was fueled by some strong results hinting at how very important these spaces are. We list only a few here: 1. A Banach space X contains an isomorph of Co if and only if there is a sequence {xn}::"=l in
X such that
I: Ix'(xn)1
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