Jensen's inequality for partial traces in von Neumann algebras

TL;DR

This paper extends Jensen's inequality for partial traces from finite-dimensional spaces to semifinite and general von Neumann algebras, broadening its mathematical applicability.

Contribution

It introduces a Jensen's inequality for partial traces in both semifinite and non-tracial von Neumann algebras, generalizing previous finite-dimensional results.

Findings

Jensen's inequality established for partial traces in semifinite von Neumann algebras.

Extension of the inequality to non-tracial von Neumann algebras.

Broadens the theoretical framework for operator inequalities in infinite-dimensional settings.

Abstract

Motivated by a recent result on finite-dimensional Hilbert spaces, we prove a Jensen's inequality for partial traces in semifinite von Neumann algebras. We also prove a similar inequality in the framework of general (non-tracial) von Neumann algebras.