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• W1539016502 abstract "A remarkable theorem of R. C. James is the following: suppose that $X$ is a Banach space and $C subseteq X$ is a norm bounded, closed and convex set such that every linear functional $x^* in X^*$ attains its supremum on $C$; then $C$ is a weakly compact set. Actually, this result is significantly stronger than this statement; indeed, the proof can be used to obtain other surprising results. For example, suppose that $X$ is a separable Banach space and $S$ is a norm separable subset of the unit ball of $X^*$ such that for each $x in X$ there exists $x^* in S$ such that $x^*(x) = |x|$ then $X^*$ is itself norm separable . If we call $S$ a support set, in this case, with respect to the entire space $X$, one can ask questions about the size and structure of a support set, a support set not only with respect to $X$ itself but perhaps with respect to some other subset of $X$@. We analyze one particular case of this as well as give some applications." @default.
• W1539016502 created "2016-06-24" @default.
• W1539016502 creator A5084423659 @default.
• W1539016502 date "1993-03-04" @default.
• W1539016502 modified "2023-09-27" @default.
• W1539016502 title "Spaces Of Lipschitz Functions On Banach Spaces" @default.
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