Pei-Kee Lin

Köthe-Bochner Function Spaces (eBook, PDF)

• Format: PDF

Produktbeschreibung

This monograph is devoted to the study of Köthe-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 Köthe-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.

---

Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.

Produktdetails

• Verlag: Birkhäuser Boston
• Seitenzahl: 370
• Erscheinungstermin: 27. Juni 2011
• Englisch
• ISBN-13: 9780817681883
• Artikelnr.: 44198171

Inhaltsangabe

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.

Rezensionen

From the reviews: "This book is a nice and useful reference for researchers in functional analysis who wish to have a quite comprehensive survey of geometric properties of Banach spaces of vector-valued functions." ---Mathematical Reviews "This book ... gives in fact an exhaustive and very up-to-date account of several aspects of the general theory (isomorphic) and geometry of Banach spaces. This book is self-contained with an exhaustive list of references at the end of each chapter. Apart from well thought-out exercises at the end of each section, the `Notes and Remarks' section at the end of each chapter contains several open questions with additional comments and references. This book is worth having on the shelves of anyone interested in Banach space theory. I thoroughly enjoyed going through it."(ZENTRALBLATT MATH) "This book, though somewahte restrictively entitled, gives in fact an exhaustive and very up-to-date account of several aspects of the general theory (isomorphic) and geometry of Banach spaces. . . This book is self-contained with an exhaustive list of references at the end of each chapter. Apart from well thoght-out exervises at the end of each section,t he 'Notes and Remarks' section at the end of each chapter contains several open questions with additional somments and references. This book is worth having on the shelves of anyone interested in Banach space theory. I thoroughly enjoyed going through it." ---Zenteralblatt MATH