Orthonormal Systems and Banach Space Geometry

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Orthonormal Systems and Banach Space Geometry describes the interplay between orthonormal expansions and Banach space geometry. The text yields a detailed insight into concepts including type and co-type of Banach spaces, B-convexity, super-reflexivity, the vector-valued Fourier transform, the vector-valued Hilbert transform and the unconditionality property for martingale differences (UMD). A long list of unsolved problems is included as a starting point for research. This book should be accessible to graduate students and researchers with some basic knowledge of Banach space theory, real analysis, probability and algebra.
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Editorial Reviews

From the Publisher
'This work will certainly become a standard reference.' Zenbralblatt MATH

' … the book contains an enormous amount of information … it will serve as an invaluable reference book for years to come.' G. J. O. Jameson

' … this volume [is certain] to become a standard reference.' M. Grosser, Monatshefte für Mathematik

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Product Details

Table of Contents

Introduction 1
0 Preliminaries 4
1 Ideal norms and operator ideals 25
2 Ideal norms associated with matrices 35
3 Ideal norms associated with orthonormal systems 65
4 Rademacher and Gauss ideal norms 126
5 Trigonometric ideal norms 235
6 Walsh ideal norms 321
7 Haar ideal norms 344
8 Unconditionality 429
9 Miscellaneous 461
Summaries 509
List of symbols 514
Bibliography 523
Index 546
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