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- W2078052142 abstract "Let 2^ (resp. 2^*) be the set of all closed, convex and bounded (resp. «/-compact and convex) subsets of a Banach space E (resp. of its dual E*) furnished with the Hausdorff metric. It is shown that if there exists an equivalent norm || • || in E with dual || • ||* such that (E, ■ ) has Mazur's intersection property and (??*,|| • ||*) has iu*-Mazur's intersection property, then (1) there exists a dense G s subset % of 2^ such that for every Xe% the strongly exposing functionals form a dense Gi subset of E* ; (2) there exists a dense Gi subset 2q* of 2^* such that for every X* 6 2q* the it;-strongly exposing functionals form a dense G? subset of E. In particular every X 6 2^6 is the closed convex hull of its strongly exposed points and every X* 6 2q* is the «/-closed convex hull of its «/-strongly exposed points." @default.
- W2078052142 created "2016-06-24" @default.
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- W2078052142 date "1988-01-01" @default.
- W2078052142 modified "2023-09-26" @default.
- W2078052142 title "Mazur’s intersection property and a Kreĭn-Milcprime man type theorem for almost all closed, convex and bounded subsets of a Banach space" @default.
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- W2078052142 doi "https://doi.org/10.1090/s0002-9939-1988-0958059-3" @default.
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