An $L_p$-inequality for anticommutators

TL;DR

This paper establishes an $L_p$-inequality for anticommutators in noncommutative $L_p$-spaces and applies it to demonstrate Lipschitz continuity of noncommutative Mazur maps between these spaces.

Contribution

It introduces a fundamental inequality for anticommutators and completes the analysis of noncommutative Mazur maps' Lipschitz properties.

Findings

Proved a basic inequality involving anticommutators in noncommutative $L_p$-spaces.

Showed noncommutative Mazur maps are Lipschitz on balls for $0<q<p< $.

Abstract

We prove a basic inequality involving anticommutators in noncommutative $L_p$-spaces. We use it to complete our study of the noncommutative Mazur maps from $L_p$ to $L_q$ showing that they are Lipschitz on balls when $0<q<p<\infty$.