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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

On the structure of weakly compact subsets of Hilbert spaces and applications to the geometry of Banach spaces


Authors: S. Argyros and V. Farmaki
Journal: Trans. Amer. Math. Soc. 289 (1985), 409-427
MSC: Primary 46B20; Secondary 46C10
MathSciNet review: 779073
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Abstract: A characterization of weakly compact subsets of a Hilbert space, when they are considered as subsets of $ B$-spaces with an unconditional basis, is given. We apply this result to renorm a class of reflexive $ B$-spaces by defining a norm uniformly convex in every direction. We also prove certain results related to the factorization of operators. Finally, we investigate the structure of weakly compact subsets of $ {L^1}(\mu )$.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0779073-9
Article copyright: © Copyright 1985 American Mathematical Society