An Isometric Representation of the Dual of
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Authors: | S Verwulgen |
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Institution: | (1) Departement of Mathematics, University of Antwerp, Middleheimlaan 1, Antwerp, 2020, Belgium |
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Abstract: | Many structures in functional analysis are introduced as the limit of an inverse (aka projective) system of seminormed spaces 2, 3, 8]. In these situations, the dual is moreover equipped with a seminorm. Although the topology of the inverse limit is seldom metrizable, there is always a natural overlying locally convex approach structure. We provide a method for computing the adjoint of this space, by showing that the dual of a limit of locally convex approach spaces becomes a co-limit in the category of seminormed spaces. As an application we obtain an isometric representation of the dual space of real valued continuous functions on a locally compact Hausdorff space X, equipped with the compact open structure. |
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Keywords: | 46M40 46A03 46E27 28A33 |
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