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Journal of Convex Analysis 24 (2017), No. 2, 587--619
Copyright Heldermann Verlag 2017

Hahn-Banach Theorem and Duality Theory on non-Archimedean Locally Convex Spaces

Tomoki Mihara
Dept. of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

Let k be a local field with valuation ring O and residue field r(k). We extend Hahn-Banach theorem for the class of seminormed k-vector spaces to several classes of locally convex spaces and subspaces over k, O, and r(k). We establish continuous duality theory for several classes of locally convex spaces over k, O, and r(k).

Keywords: p-adic analysis, Hahn-Banach theorem, duality theory.

MSC: 11S23, 46B10, 16D90

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