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

Tomoki Mihara

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

Number Theory 2016-03-23 v2 Functional Analysis Operator Algebras

Authors: Tomoki Mihara

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 $\overline{k}$ .

Keywords

Hahn-Banach theorem non-Archimedean locally convex space local field seminormed vector space Iwasawa-type duality valuation ring residue field

Cite

@article{arxiv.1504.04488,
  title  = {Hahn--Banach Theorem and Duality Theory on non-Archimedean Locally Convex Spaces},
  author = {Tomoki Mihara},
  journal= {arXiv preprint arXiv:1504.04488},
  year   = {2016}
}

Comments

Readers pointed out that several results in my article (e.g. Theorem 2.8 for the case $L$ is separable or seminormed case) are well-know and hence references should be completed. Then the content of this article is completly changed. Instead, a related (but not the same) paper will be published in Journal of Convex Analysis Vol. 24 (2017) in a way in accordance with the publication policy of the journal

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

Abstract

Keywords

Cite

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