On strongly exposing functionals

Borwein, J. M.

doi:10.1090/S0002-9939-1978-0493272-7

On strongly exposing functionals
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Proc. Amer. Math. Soc. 69 (1978), 46-48 Request permission

Abstract:

Let K be a weakly compact convex set. The recent result of Lau that its strongly exposing functionals form a dense ${G_\delta }$ is here proved by a modification of Lindenstrauss’s proof that K is the closed convex hull of its strongly exposed points.

References

J. Bourgain, Strongly exposed points in weakly compact convex sets in Banach spaces, Proc. Amer. Math. Soc. 58 (1976), 197–200. MR 415272, DOI 10.1090/S0002-9939-1976-0415272-3
Joseph Diestel, Geometry of Banach spaces—selected topics, Lecture Notes in Mathematics, Vol. 485, Springer-Verlag, Berlin-New York, 1975. MR 0461094
Ka Sing Lau, On strongly exposing functionals, J. Austral. Math. Soc. Ser. A 21 (1976), no. 3, 362–367. MR 423049, DOI 10.1017/s1446788700018656
Ka Sing Lau, A remark on strongly exposing functionals, Proc. Amer. Math. Soc. 59 (1976), no. 2, 242–244. MR 415274, DOI 10.1090/S0002-9939-1976-0415274-7

On operators which achieve their norm

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