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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Rotundity, the C.S.R.P., and the $ \lambda$-property in Banach spaces


Authors: Richard M. Aron, Robert H. Lohman and Antonio Suárez
Journal: Proc. Amer. Math. Soc. 111 (1991), 151-155
MSC: Primary 46B20; Secondary 46E30
MathSciNet review: 1030732
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Abstract: Two open questions stemming from the $ \lambda $-property in Banach spaces are solved. The following are shown to be equivalent in a Banach space $ X$: (a) $ X$ has the $ \lambda $-property; (b) every vector in the closed unit ball of $ X$ is expressible as a convex series of extreme points of the unit ball of $ X$. Also, by exhibiting a class of nonrotund Orlicz spaces for which the $ \lambda $-function is identically 1 on the unit spheres, we answer negatively the question of whether the $ \lambda $-function characterizes rotund Banach spaces.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1030732-0
PII: S 0002-9939(1991)1030732-0
Keywords: $ \lambda $-property, extreme point, convex series, Orlicz spaces, rotund Banach spaces
Article copyright: © Copyright 1991 American Mathematical Society