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Transactions of the American Mathematical Society

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

 

 

$ B$-convexity and reflexivity in Banach spaces


Author: Dean R. Brown
Journal: Trans. Amer. Math. Soc. 187 (1974), 69-76
MSC: Primary 46B10
DOI: https://doi.org/10.1090/S0002-9947-1974-0333677-9
MathSciNet review: 0333677
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Abstract: A proof of James that uniformly nonsquare spaces are reflexive is extended in part to B-convex spaces. A condition sufficient for non-B-convexity and related conditions equivalent to non-B-convexity are given. The following theorem is proved: A Banach space is B-convex if each subspace with basis is B-convex.


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DOI: https://doi.org/10.1090/S0002-9947-1974-0333677-9
Keywords: B-convexity, reflexivity, P-convexity, uniform-convexity, uniformly nonsquare, uniformly non $ 1_{n}^{(1)}$, geometry of the unit ball, Schauder basis
Article copyright: © Copyright 1974 American Mathematical Society