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Compactoid sets in p-adic locally convex spaces with the Hahn-Banach extension property. (English) Zbl 0675.46040

Summary: Let K be a non-archimedean, non-trivially valued, complete field with valuation \(| \cdot |\). Given a locally convex space E over K with the H.B.E.P., we obtain several descriptions of compactoid sets of E in terms of non-archimedean seminorms on the topological dual \(E'\).

MSC:

46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis
46A20 Duality theory for topological vector spaces
46A50 Compactness in topological linear spaces; angelic spaces, etc.
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