2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152825Let $E$ 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.Functional Analysis46Btext