An inequality in noncommutative $L_p$-spaces

TL;DR

This paper proves a contraction property of the difference between the identity and a trace-preserving conditional expectation on noncommutative Lp-spaces for p>2, revealing a new inequality in this mathematical setting.

Contribution

It establishes a novel inequality showing that Id - E is a contraction on the positive cone in noncommutative Lp-spaces for p>2, extending understanding of operator inequalities.

Findings

Id - E is a contraction on the positive cone for p>2

New inequality in noncommutative Lp-spaces

Extension of classical inequalities to noncommutative setting

Abstract

We prove that for any (trace-preserving) conditional expectation $\mathcal E$ on a noncommutative $L_p$ with $p>2$, $Id-\mathcal E$ is a contraction on the positive cone $L_p^+$.