Abstract

Let k be a local field with valuation ring O and residue field k‾\overline{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 k‾\overline{k}. We establish continuous duality theory for several classes of locally convex spaces over k, O, and k‾\overline{k}.

Author information

Contact details are reproduced from the original publication and may be historical.

Tomoki Mihara

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

mihara.t.ab@m.titech.ac.jp

Keywords

  • p-adic analysis
  • Hahn-Banach theorem
  • duality theory

Mathematics Subject Classification

11S23, 46B10, 16D90

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Suggested citation

T. Mihara. “Hahn-Banach Theorem and Duality Theory on non-Archimedean Locally Convex Spaces.” Journal of Convex Analysis 24 (2017), No. 2, 587–619. https://doi.org/10.68381/jca24038

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Published by Heldermann Verlag, 2017. Rights now held by Banach Press.