𝐵-convexity and reflexivity in Banach spaces

Brown, Dean R.

doi:10.1090/S0002-9947-1974-0333677-9

$B$-convexity and reflexivity in Banach spaces
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by Dean R. Brown

Trans. Amer. Math. Soc. 187 (1974), 69-76

DOI: https://doi.org/10.1090/S0002-9947-1974-0333677-9

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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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