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This monograph is devoted to the study of KtheBochner function spaces anarea of research at the intersection of Banach space theory harmonic analysisprobability and operator theory. A number of significant resultsmanyscattered throughout the literatureare distilled and presented here givingreaders a comprehensive view of KtheBochner function spaces from thesubjects origins in functional analysis to its connections to otherdisciplines. Key features and topics Considerable background materialprovided including a compilation of important theorems and concepts inclassical functional analysis as well as a discussion of the DunfordPettisProperty tensor products of Banach spaces relevant geometry and the basictheory of conditional expectations and martingales Rigorous treatment ofKtheBochner spaces encompassing convexity measurability stabilityproperties DunfordPettis operators and Talagrand spaces with a particularemphasis on open problems Detailed examination of Talagrands TheoremBourgains Theorem and the DiazKalton Theorem the latter extended toarbitrary measure spaces Notes and remarks after each chapter withextensive historical information references and questions for further study Instructive examples and many exercises throughout Both expansive and precisethis books unique approach and systematic organization will appeal to advancedgraduate students and researchers in functional analysis probability operatortheory and related fields. TOCPreface. Notation. Classical Theorems.Convexity and Smoothness. K?heBochner Function Spaces. Stability PropertiesI. Stability Properties II. Continuous Function Spaces. Index. «
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