Reflexivity and the sup of linear functionals
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A relatively easy proof is given for the known theorem that a Banach space is reflexive if and only if each continuous linear functional attains its sup on the unit ball. This proof simplifies considerably for separable spaces and can be extended to give a proof that a boundedw-closed subsetX of a complete locally convex linear topological space isw-compact if and only if each continuous linear functional attains its sup onX.
KeywordsBanach Space Unit Ball Topological Vector Space Linear Functional Weak Topology
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- 2.R. C. James,Bases and reflexivity of Banach spaces, Bull. Amer. Math Soc.56 (1950), 58 (abstract 80).Google Scholar