On weak compactness in 𝐿¹(𝜇,𝑋)

Author:

Diestel J.,Ruess W. M.,Schachermayer W.

Abstract

We present a characterization of weak compactness in L 1 ( μ , X ) {L^1}(\mu ,X) and in more general Banach spaces of vector-valued measurable functions. Moreover, we slightly refine Talagrand’s parametrized version of Rosenthal’s l 1 {l^1} -theorem and extend it to L 1 ( μ , X ) {L^1}(\mu ,X) -bounded sequences.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference12 articles.

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3. Mathematical Surveys, No. 15;Diestel, J.,1977

4. Sur les espaces de Köthe;Dieudonné, Jean;J. Analyse Math.,1951

5. N. Dunford and J.T. Schwartz, Linear operators, Part 1, Interscience, New York, 1958.

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