Operators preserving orthogonality are isometries

Alexander Koldobsky

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arXiv · math/9212203

Operators preserving orthogonality are isometries

Alexander Koldobsky

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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 $\|x+αy\|\geq \|x\|$ for every $α\in R$. We prove that every operator from $E$ into itself preserving orthogonality is an isometry multiplied by a constant.

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Alexander Koldobsky. 1992-12-04. Operators preserving orthogonality are isometries. https://arxiv.org/abs/math/9212203

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