A metric characterization of normed linear spaces

Timur Oikhberg, Haskell Rosenthal

Research output: Contribution to journalArticlepeer-review

Abstract

Let X be a linear space over a field K = R or C, equipped with a metric ρ. It is proved that ρ is induced by a norm provided it is translation invariant, real scalar "separately" continuous, such that every 1-dimensional subspace of X is isometric to K in its natural metric, and (in the complex case) ρ(x, y) = p(ix, iy) for any x, y ∈ X.

Original languageEnglish (US)
Pages (from-to)597-608
Number of pages12
JournalRocky Mountain Journal of Mathematics
Volume37
Issue number2
DOIs
StatePublished - 2007
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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