
Journal of Convex Analysis 24 (2017), No. 2, 587619 Copyright Heldermann Verlag 2017 HahnBanach Theorem and Duality Theory on nonArchimedean Locally Convex Spaces Tomoki Mihara Dept. of Mathematics, Tokyo Institute of Technology, 2121 Ookayama, Meguroku, Tokyo 1528551, Japan mihara.t.ab@m.titech.ac.jp Let k be a local field with valuation ring O and residue field r(k). We extend HahnBanach theorem for the class of seminormed kvector 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: padic analysis, HahnBanach theorem, duality theory. MSC: 11S23, 46B10, 16D90 [ Fulltextpdf (300 KB)] for subscribers only. 