Description
BIRKHAUSER Koethe-Bochner Function Spaces 2004 Edition by Pei-Kee Lin
This monograph is devoted to the study of Koethe-Bochner function spaces an active area of research at the intersection of Banach space theory harmonic analysis probability and operator theory. A number of significant results---many scattered throughout the literature---are distilled and presented here giving readers a comprehensive view of the subject from its origins in functional analysis to its connections to other disciplines. Considerable background material is provided and the theory of Koethe-Bochner spaces is rigorously developed with a particular focus on open problems. Extensive historical information references and questions for further study are included; instructive examples and many exercises are incorporated throughout. 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. Table of contents : 1 Classical Theorems.- 1.1 Preliminaries.- 1.2 Basic Sequences.- 1.3 Banach Spaces Containing l1 or c0.- 1.4 James's Theorem.- 1.5 Continuous Function Spaces.- 1.6 The Dunford-Pettis Property.- 1.7 The Pe?czynski Property (V*).- 1.8 Tensor Products of Banach Spaces.- 1.9 Conditional Expectation and Martingales.- 1.10 Notes and Remarks.- 1.11 References.- 2 Convexity and Smoothness.- 2.1 Strict Convexity and Uniform Convexity.- 2.2 Smoothness.- 2.3 Banach-Saks Property.- 2.4 Notes and Remarks.- 2.5 References.- 3 Koethe-Bochner Function Spaces.- 3.1 Koethe Function Spaces.- 3.2 Strongly and Scalarly Measurable Functions.- 3.3 Vector Measure.- 3.4 Some Basic Results.- 3.5 Dunford-Pettis Operators.- 3.6 The Radon-Nikodym Property.- 3.7 Notes and Remarks.- 3.8 References.- 4 Stability Properties I.- 4.1 Extreme Points and Smooth Points.- 4.2 Strongly Extreme and Denting Points.- 4.3 Strongly and w*-Strongly Exposed Points.- 4.4 Notes and Remarks.- 4.5 References.- 5 Stability Properties II.- 5.1 Copies of c0 in E(X).- 5.2 The Diaz-Kalton Theorem.- 5.3 Talagrand's L1(X)-Theorem.- 5.4 Property (V*).- 5.5 The Talagrand Spaces.- 5.6 The Banach-Saks Property.- 5.7 Notes and Remarks.- 5.8 References.- 6 Continuous Function Spaces.- 6.1 Vector-Valued Continuous Functions.- 6.2 The Dieudonne Property in C(K X).- 6.3 The Hereditary Dunford-Pettis Property.- 6.4 Projective Tensor Products.- 6.5 Notes and Remarks.- 6.6 References.