Geodesic
Hahn-Banach Theorem and Duality Theory on non-Archimedean Locally Convex Spaces
Journal of convex analysis, Tome 24 (2017) no. 2, pp. 587-619
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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).
Classification : 11S23, 46B10, 16D90
Mots-clés : p-adic analysis, Hahn-Banach theorem, duality theory 
@article{JCA_2017_24_2_JCA_2017_24_2_a14,
     author = {T. Mihara},
     title = {Hahn-Banach {Theorem} and {Duality} {Theory} on {non-Archimedean} {Locally} {Convex} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {587--619},
     year = {2017},
     volume = {24},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a14/}
}
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T. Mihara. Hahn-Banach Theorem and Duality Theory on non-Archimedean Locally Convex Spaces. Journal of convex analysis, Tome 24 (2017) no. 2, pp. 587-619. http://geodesic.mathdoc.fr/item/JCA_2017_24_2_JCA_2017_24_2_a14/