A remark on strongly exposing functionals
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- by Ka Sing Lau PDF
- Proc. Amer. Math. Soc. 59 (1976), 242-244 Request permission
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
- R. Anantharaman, On exposed points of the range of a vector measure. II, Proc. Amer. Math. Soc. 55 (1976), no. 2, 334–338. MR 399851, DOI 10.1090/S0002-9939-1976-0399851-8
- M. Edelstein and J. E. Lewis, On exposed and farthest points in normed linear spaces, J. Austral. Math. Soc. 12 (1971), 301–308. MR 0310596
- Ka Sing Lau, Farthest points in weakly compact sets, Israel J. Math. 22 (1975), no. 2, 168–174. MR 394126, DOI 10.1007/BF02760164 —, On strongly exposing functionals, J. Austral. Math. Soc. (to appear).
- Joram Lindenstrauss, On operators which attain their norm, Israel J. Math. 1 (1963), 139–148. MR 160094, DOI 10.1007/BF02759700
- S. L. Troyanski, On locally uniformly convex and differentiable norms in certain non-separable Banach spaces, Studia Math. 37 (1970/71), 173–180. MR 306873, DOI 10.4064/sm-37-2-173-180
Additional Information
- © Copyright 1976 American Mathematical Society
- 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