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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Verwulgen, S. An Isometric Representation of the Dual of \( {\user1{\mathcal{C}}}{\left( {X,\mathbb{R}} \right)} \) . Appl Categor Struct 14, 111–121 (2006). https://doi.org/10.1007/s10485-005-9007-2
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DOI: https://doi.org/10.1007/s10485-005-9007-2