Weak compactness in

Author:
A. Ülger

Journal:
Proc. Amer. Math. Soc. **113** (1991), 143-149

MSC:
Primary 46E40; Secondary 46B20

DOI:
https://doi.org/10.1090/S0002-9939-1991-1070533-0

MathSciNet review:
1070533

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Abstract: Let be a probability space, a Banach space, and the Banach space of Bochner integrable functions . Let . In this paper we characterize the rwc (relatively weakly compact) subsets of . The main results are as follows:

**Theorem A**. *A subset* *of* *is rwc iff given any sequence* *in* *there exists a sequence* , with *such that, for a.e.* *in* , *the sequence* *converges weakly in* .

**Theorem B**. *A subset* *of* *is rwc iff given any* *there exist an integer* *and a rwc subset* *of NW such that* , *where* *is the unit ball of* .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1070533-0

Keywords:
Bochner integrable functions,
weak compactness

Article copyright:
© Copyright 1991
American Mathematical Society