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Proceedings of the American Mathematical Society

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

 

 

The dual of a theorem of Bishop and Phelps


Author: George Luna
Journal: Proc. Amer. Math. Soc. 47 (1975), 171-174
DOI: https://doi.org/10.1090/S0002-9939-1975-0355554-6
MathSciNet review: 0355554
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Abstract: We dualize a theorem of Bishop and Phelps by showing that in the dual of a Banach space the intersection of a weak* closed finite codimensional linear variety and a weak* closed convex subset $ C$ contains a norm dense set of weak* support points of $ C$. We use this theorem to obtain a result which is related to an abstract approximation problem of Deutsch and Morris.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0355554-6
Keywords: Bishop-Phelps, weak* support point, abstract approximation, approximation and interpolation, norm preserving approximation
Article copyright: © Copyright 1975 American Mathematical Society