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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ P$-convexity and $ B$-convexity in Banach spaces


Author: Dean R. Brown
Journal: Trans. Amer. Math. Soc. 187 (1974), 77-81
MSC: Primary 46B10
MathSciNet review: 0333678
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Abstract: Two properties of B-convexity are shown to hold for P-convexity:

(1) Under certain conditions, the direct sum of two P-convex spaces is P-convex.

(2) A Banach space is P-convex if each subspace having a Schauder decomposition into finite dimensional subspaces is P-convex.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1974-0333678-0
PII: S 0002-9947(1974)0333678-0
Keywords: B-convexity, P-convexity, reflexivity, uniform convexity, geometry of the unit ball, Ramsey's theorem, Schauder basis, Schauder decomposition
Article copyright: © Copyright 1974 American Mathematical Society