On New Notions of Orthogonality in Normed Spaces via the 2-HH-Norms

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Kikianty, Eder and Dragomir, Sever S (2009) On New Notions of Orthogonality in Normed Spaces via the 2-HH-Norms. Research report collection, 12 (1).

Abstract

Kikianty and Dragomir in 2008 introduced the p-HH-norms on the Cartesian product of two copies of a normed space, which are equivalent to the well-known p-norms. In this paper, notions of orthogonality in terms of 2-HH-norms are introduced. The main properties of these orthogonalities are discussed. Several characterizations of inner product spaces are established, as well as the characterization of strictly convex spaces.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/17678
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords orthogonality, Pythagorean orthogonality, Isosceles orthogonality, inner product space, strictly convex space, Cartesian product space
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