Jensen's inequality for partial traces in von Neumann algebras

2025/07/03 by Rahaman, Mizanur, Turowska, Lyudmila
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Probability (math.PR) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2507.02422

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.

Citations

• A Jensen inequality for partial traces and applications to partially semiclassical limits
• Jensen's trace inequality in several variables
• Jensen's Operator Inequality
• A schwarz inequality for positive linear maps on C^∗-algebras

Related

• Jensen's trace inequality in several variables
• A generalization of the inequality of Audenaert et al
• Young's Inequality in Semifinite von Neumann Algebras
• Jensen's Operator Inequality
• A Jensen inequality for partial traces and applications to partially semiclassical limits