The dual of a theorem of Bishop and Phelps-Reference-Cited by-同舟云学术

The dual of a theorem of Bishop and Phelps

Published:1975 Issue:1 Volume:47 Page:171-174
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Luna George

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 C contains a norm dense set of weak* support points of C C . We use this theorem to obtain a result which is related to an abstract approximation problem of Deutsch and Morris.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1975-047-01/S0002-9939-1975-0355554-6/S0002-9939-1975-0355554-6.pdf

Reference6 articles.

1. The support functionals of a convex set;Bishop, Errett,1963

2. On simultaneous approximation and interpolation which preserves the norm;Deutsch, Frank;J. Approximation Theory,1969

3. A geometrical approach to property (SAIN);Holmes, Richard;J. Approximation Theory,1973

4. Simultaneous approximation and interpolation in 𝑙₁;Lambert, Joseph M.;Proc. Amer. Math. Soc.,1972

5. Weak* support points of convex sets in 𝐸*;Phelps, R. R.;Israel J. Math.,1964

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. The Bishop–Phelps Theorem;10 Mathematical Essays on Approximation in Analysis and Topology;2005

2. Simultaneous Interpolation and Norm-Preservation;Delay Equations, Approximation and Application;1985