The canonical partial metric and the uniform convexity on normed spaces
Submitted: 2013-11-25
|Accepted: 2013-11-25
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Keywords:
Partial metric, Convexity, Normed spaces
Supporting agencies:
Generalidad Valenciana
grant GV04B-371
the Spanish Ministry of Science and Technology
Plan Nacional I D I
grant BFM2003-02302
and FEDER
and the Polytechnical University of Valencia
Abstract:
In this paper we introduce the notion of canonical partial metric associated to a norm to study geometric properties of normed spaces. In particular, we characterize strict convexity and uniform convexity of normed spaces in terms of the canonical partial metric defined by its norm.
We prove that these geometric properties can be considered, in this sense, as topological properties that appear when we compare the natural metric topology of the space with the non translation invariant topology induced by the canonical partial metric in the normed space.
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