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

DOI:
https://doi.org/10.1090/S0002-9947-1985-0779073-9

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 -spaces with an unconditional basis, is given. We apply this result to renorm a class of reflexive -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 .

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DOI:
https://doi.org/10.1090/S0002-9947-1985-0779073-9

Article copyright:
© Copyright 1985
American Mathematical Society