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