Banach Spaces of Vector-Valued Functions

1. Front Matter

   Pages I-VIII

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2. Introduction

   • Pilar Cembranos, José Mendoza

   Pages 1-8

3. Preliminaries

   • Pilar Cembranos, José Mendoza

   Pages 9-40

4. Copies of c ₀ and ℓ₁ in L _p (μ, X)

   • Pilar Cembranos, José Mendoza

   Pages 41-63

5. C(K, X) spaces

   • Pilar Cembranos, José Mendoza

   Pages 65-74

6. L _p (μ, X) spaces

   • Pilar Cembranos, José Mendoza

   Pages 75-82

7. The space L _∞( μ, X)

   • Pilar Cembranos, José Mendoza

   Pages 83-104

8. Tabulation of results

   • Pilar Cembranos, José Mendoza

   Pages 105-106

9. Some related open problems

   • Pilar Cembranos, José Mendoza

   Pages 107-109

10. Back Matter

    Pages 111-118

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"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.

• Banach space
• classical sequence
• functional analysis
• operator theory
• space

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