Operators preserving orthogonality are isometries

Details Operators preserving orthogonality are isometries Operators preserving orthogonality are isometries

1992-12-04

arxiv.org/abs/math/9212203v1

Mathematics

Functional Analysis

Scientific paper

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.

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