Banach Spaces of Vector-Valued Functions

Pilar Cembranos, José Mendoza (auth.)3540637451, 9783540637455

“When do the Lebesgue-Bochner function spaces contain a copy or a complemented copy of any of the classical sequence spaces?” This problem and the analogous one for vector- valued continuous function spaces have attracted quite a lot of research activity in the last twenty-five years. The aim of this monograph is to give a detailed exposition of the answers to these questions, providing a unified and self-contained treatment. It presents a great number of results, methods and techniques, which are useful for any researcher in Banach spaces and, in general, in Functional Analysis. This book is written at a graduate student level, assuming the basics in Banach space theory.

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Table of contents :
Introduction….Pages 1-8
Preliminaries….Pages 9-40
Copies of c 0 and ℓ 1 in L p (μ, X )….Pages 41-63
C(K, X) spaces….Pages 65-74
L p (μ, X ) spaces….Pages 75-82
The space L ∞ (μ, X )….Pages 83-104
Tabulation of results….Pages 105-106
Some related open problems….Pages 107-109