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Proceedings of the American Mathematical Society

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Compactness of sets of integrable functions with values in a Banach space


Author: Atle Seierstad
Journal: Proc. Amer. Math. Soc. 52 (1975), 204-208
MSC: Primary 46E40; Secondary 46G99
DOI: https://doi.org/10.1090/S0002-9939-1975-0470676-7
MathSciNet review: 0470676
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Abstract: The present paper gives direct proofs of compactness (in a pairing topology) of bounded sets of strongly integrable functions with values in weakly compact subsets of a Banach space. The pairing in question is that one defined by the integral of the scalar product of two strongly integrable functions with values in the Banach space and its dual, respectively.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0470676-7
Article copyright: © Copyright 1975 American Mathematical Society