Operators preserving orthogonality are isometries

Alexander Koldobsky

Operators preserving orthogonality are isometries

Functional Analysis 2008-02-03 v1

Authors: Alexander Koldobsky

Abstract

Let $E$ be a real Banach space. For $x,y \in E,$ we follow R.James in saying that $x$ is orthogonal to $y$ if $\|x+\alpha y\|\geq \|x\|$ for every $\alpha \in R$ . We prove that every operator from $E$ into itself preserving orthogonality is an isometry multiplied by a constant.

Keywords

operator theory on banach spaces banach space operator theory

Cite

@article{arxiv.math/9212203,
  title  = {Operators preserving orthogonality are isometries},
  author = {Alexander Koldobsky},
  journal= {arXiv preprint arXiv:math/9212203},
  year   = {2008}
}

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