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

Tomoki Mihara

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arXiv · 1504.04488

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

Tomoki Mihara

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Abstract

Let $k$ be a local field with valuation ring $O_k$ and residue field $\overline{k}$. We extend Hahn--Banach theorem for the class of seminormed $k$-vector spaces to several classes of locally convex spaces and subspaces over $k$, $O_k$, and $\overline{k}$. We establish analogues of Iwasawa-type duality for several classes of locally convex spaces over $k$, $O_k$, and $\overline{k}$.

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BibTeX RIS

Tomoki Mihara. 2015-04-17. Hahn--Banach Theorem and Duality Theory on non-Archimedean Locally Convex Spaces. https://arxiv.org/abs/1504.04488

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