Hahn-Banach theorems for κ-normed spaces

2003/01/18 by S. V. Lüdkovsky, S. V. Ludkovsky, Ludkovsky, S. V. +2
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #Fixed Point Theorems Analysis #math.FA #msc:52A07 #msc:57N17

paper · pdf · doi:10.48550/arxiv.math/0301197

Latex, 18 pages

arxiv created 2003/01/18 · arxiv updated 2009/11/30

Abstract

For a new class of topological vector spaces, namely κ-normed spaces, and associated quasisemilinear topological preordered space is defined and investigated. This structure arise naturally from the consideration of a κ-norm, that is a distance function between a point and a G_δ-subset. For it, analogs of the Hahn-Banach theorem are proved.

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