Köthe-Bochner Function Spaces

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 Köthe-Bochner Function Spaces.- 3.1 Köthe 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-Nikodým 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 Díaz-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 Dieudonné 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.