A characterization of inner product spaces

zbMATH Open1237.46008arXiv1009.0079MaRDI QIDQ5199879

John M. Rassias, Mohammad Sal Moslehian

Publication date: 16 August 2011

Abstract: In this paper we present a new criterion on characterization of real inner product spaces. We conclude that a real normed space $(X,|...|)$ is an inner product space if ${\displaystyle }$sum_{epsilon_i in {-1,1}} |x_1 + sum_{i=2}^kepsilon_ix_i|^2=sum_{epsilon_i in {-1,1}} (|x_1| + sum_{i=2}^kepsilon_i|x_i|)^2,${\displaystyle }$ for some positive integer $kgeq2$ and all $x_1,...,x_{k}inX$. Conversely, if $(X,|...|)$ is an inner product space, then the equality above holds for all $kgeq2$ and all $x_1,...,x_{k}inX$.

Full work available at URL: https://arxiv.org/abs/1009.0079

zbMATH Keywords

characterization of real inner product spaces

Mathematics Subject Classification ID

Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) (46C05) Geometry and structure of normed linear spaces (46B20) Characterizations of Hilbert spaces (46C15)

Related Items (7)

A Characterization of Inner Product Spaces ⋮ Title not available (Why is that?) ⋮ Title not available (Why is that?) ⋮ Title not available (Why is that?) ⋮ Title not available (Why is that?) ⋮ Characterization of inner product spaces by means of orthogonally additive mappings ⋮ Title not available (Why is that?)

This page was built for publication: A characterization of inner product spaces

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5199879)