2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229652In this short note we give a short proof of a recent result by Potapov and Sukochev (arXiv:0904.4095v1), stating that a Lipschitz function on the real line remains Lipschitz on the (self-adjoint part of) non-commutative $L_p$ spaces with $1<p<\infty$.3 pagesFunctional AnalysisOperator Algebras47A60; 47B10A shorter proof of a result by Potapov and Sukochev on Lipschtiz functions on $S^p$text