A shorter proof of a result by Potapov and Sukochev on Lipschtiz functions on $S^p$

TL;DR

This paper presents a concise proof that Lipschitz functions on the real line retain their Lipschitz property when extended to the self-adjoint part of non-commutative Lp spaces for 1<p<∞, simplifying previous proofs.

Contribution

It provides a shorter, more elegant proof of a known result regarding Lipschitz functions on non-commutative Lp spaces, improving proof efficiency.

Findings

Lipschitz functions on the real line are Lipschitz on non-commutative Lp spaces

The proof simplifies understanding of Lipschitz continuity in non-commutative analysis

The result holds for all p between 1 and infinity, excluding endpoints.

Abstract

In 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 $1<p<\infty$.