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About: Dixmier-Ng Theorem     Goto   Sponge   NotDistinct   Permalink

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In functional analysis, the Dixmier-Ng Theorem is a characterization of when a normed space is in fact a dual Banach space. Dixmier-Ng Theorem. Let be a normed space. The following are equivalent: 1. * There exists a Hausdorff locally convex topology on so that the closed unit ball, , of is -compact. 2. * There exists a Banach space so that is isometrically isomorphic to the dual of . That 2. implies 1. is an application of the Banach–Alaoglu theorem, setting to the Weak-* topology. That 1. implies 2. is an application of the Bipolar theorem.