B-Convexity and Reflexivity in Banach Spaces

B-Convexity and Reflexivity in Banach Spaces

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...

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Veröffentlicht in:Transactions of the American Mathematical Society 1974-01, Vol.187, p.69-76, Article 69
1. Verfasser: Brown, Dean R.
Format: Artikel
Sprache:eng
Schlagworte:
Banach space
Convexity
Integers
Mathematical theorems
Numbers
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Zusammenfassung: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.
ISSN:0002-9947
1088-6850
DOI:10.2307/1997041