Abstract: In this article, a duality of k-normed topological vector spaces X is defined and investigated, where X is over the field or C
or a field with a non-trivial non-archimedean valuation. For such spaces the
analog of the Mackey-Arens theorem is proved. A conditionalk-normability
of spaces of linear topological
homeomorphisms of a locally convex k-normed
space X is studied, when an image of
elements under the corresponding operations is in Cases, whenk-normability of a topological vector space implies its
local convexity, are investigated. Applications of k-normed spaces for resolutions of differential
equations and for approximations of functions in mathematical economy are
illustrated.
Keywords and phrases: duality of spaces, space topology.
spaces, 
