Banach Function Spaces Of Vector Valued Functions

Banach Function Spaces of Vector-valued Functions

Banach Spaces of Vector-Valued Functions

"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 Function Spaces of Vector Valued Functions

The study of Banach spaces is considered, the elem nts of which are classes of measurable functions defined on a locally compact Hausdorff space with values in a fixed Banach space. Th norms of the spaces tudied are expressed in terms of length functions defined for positive measurable functions. Certain properties of the length function and the range space of the vector valued functions are reflected in the Banach function space. A representation is established of the dual spaces of these Banach function spaces in certain cases. (Author).