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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A remark on strongly exposing functionals


Author: Ka Sing Lau
Journal: Proc. Amer. Math. Soc. 59 (1976), 242-244
MSC: Primary 46B05
DOI: https://doi.org/10.1090/S0002-9939-1976-0415274-7
MathSciNet review: 0415274
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Abstract: By using the concept of farthest points, we show that the set of strongly exposing functionals of a weakly compact convex subset in a Banach space $ X$ is a dense $ {G_\delta }$ in $ {X^{\ast}}$. The construction also gives a new proof of existence of strongly exposed points in weakly compact convex sets.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0415274-7
Keywords: Banach spaces, farthest points, locally uniformly convex, strongly exposed points, strongly exposing functionals
Article copyright: © Copyright 1976 American Mathematical Society