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

Argyros, S.; Farmaki, V.

doi:10.1090/S0002-9947-1985-0779073-9

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 ${L^1}(\mu )$ .

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