Kothe-Bochner Function Spaces

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ISBN: 9780817635213 | 0817635211
Cover: Hardcover
Copyright: 1/1/2004

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"Both expansive and precise, this book's unique approach and systematic organization will appeal to advanced graduate students and researchers in functional analysis, probability, operator theory, and related fields."--BOOK JACKET.

Preface

vii

Notation

1 Classical Theorems

(100)

1.1 Preliminaries

(7)

1.2 Basic sequences

(21)

1.3 Banach Spaces Containing l1 or co

(13)

1.4 James's Theorem

(6)

1.5 Continuous Function Spaces

(9)

1.6 The Dunford-Pettis Property

(12)

1.7 The Pelczynski Property (V*)

(5)

1.8 Tensor Products of Banach Spaces

(7)

1.9 Conditional Expectation and Martingales

(13)

1.10 Notes and Remarks

(2)

1.11 References

(5)

2 Convexity and smoothness

101

(42)

2.1 Strict Convexity and Uniform Convexity

101

(23)

2.2 Smoothness

124

(6)

2.3 Banach-Saks Property

130

(7)

2.4 Notes and Remarks

137

(2)

2.5 References

139

(4)

3 Köthe-Bochner Function Spaces

143

(76)

3.1 Köthe Function Spaces

143

(19)

3.2 Strongly and Scalarly Measurable Functions

162

(5)

3.3 Vector Measure

167

(10)

3.4 Some Basic Results

177

(11)

3.5 Dunford-Pettis Operators

188

(7)

3.6 The Radon-Nikodym Property

195

(16)

3.7 Notes and Remarks

211

(5)

3.8 References

216

(3)

4 Stability Properties I

219

(28)

4.1 Extreme Points and Smooth Points

219

(7)

4.2 Strongly Extreme and Denting Points

226

(7)

4.3 Strongly and w*-Strongly Exposed Points

233

(9)

4.4 Notes and Remarks

242

(3)

4.5 References

245

(2)

5 Stability Properties II

247

(66)

5.1 Copies of co in E(X)

248

(9)

5.2 The Diaz-Kalton Theorem

257

(4)

5.3 Talagrand's Ll (X)-Theorem

261

(17)

5.4 Property (V*)

278

(12)

5.5 The Talagrand Spaces

290

(5)

5.6 The Banach-Saks Property

295

(12)

5.7 Notes and Remarks

307

(2)

5.8 References

309

(4)

6 Continuous Function Spaces

313

(54)

6.1 Vector-Valued Continuous Functions

313

(13)

6.2 The Dieudonné Property in C(K, X)

326

(5)

6.3 The Hereditary Dunford-Pettis Property

331

(17)

6.4 Projective Tensor Products

348

(7)

6.5 Notes and Remarks

355

(8)

6.6 References

363

(4)

Index

367

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Kothe-Bochner Function Spaces

Summary

Table of Contents

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Kothe-Bochner Function Spaces

Summary

Table of Contents

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