Quantified functional analysis: recapturing the dual unit ball |
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Authors: | M. Sioen S. Verwulgen |
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Affiliation: | 1. Departement Wiskunde en Informatica, Vrije Universiteit Brussel, Pleinlaan 2, B-1050, Brussel 2. Departement Wiskunde en Informatica, Universiteit Antwerpen, Middelheimlaan 1, B-2020, Antwerpen
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Abstract: | We introduce the weak approach structure for an arbitrary locally convex approach space and generalize the results from [1] about the weak approach structure of a normed space. Hereto we carefully develop the notion of a closed dual unit ball in an abstract setting (as a special kind of absolutely convex subset) because it is this kind of structure on the algebraic dual that induces, in a duality-compatible way, a locally convex approach structure on the original space. |
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