Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] R. Anantharaman, On exposed points of the range of a vector measure. II, Proc. Amer. Math. Soc. 55 (1976), 334-338. MR 0399851 (53:3693)
  • [2] M. Edelstein and J. E. Lewis, On exposed and farthest points in normed linear spaces, J. Austral. Math. Soc. 12 (1971), 301-308. MR 46 #9694. MR 0310596 (46:9694)
  • [3] K. Lau, Farthest points in weakly compact sets, Israel J. Math. 22 (1975), 168-174. MR 0394126 (52:14931)
  • [4] -, On strongly exposing functionals, J. Austral. Math. Soc. (to appear).
  • [5] J. Lindenstrauss, On operators which attain their norm, Israel J. Math. 1 (1963), 139-148. MR 28 #3308. MR 0160094 (28:3308)
  • [6] S. L. Troyanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1970/71), 173-180. MR 46 #5995. MR 0306873 (46:5995)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46B05

Retrieve articles in all journals with MSC: 46B05


Additional Information

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

American Mathematical Society