Jensen's Operator Inequality

2002/04/03 by Frank Hansen, Gert K. Pedersen · 5 citations
Mathematics · #math.OA #math.SP #msc:46L05 #msc:46L10 #msc:47A60

paper · pdf · doi:10.1112/s0024609303002200

published as Bull. London Math. Soc. 35 (2003), 553-564 · 12 pp

arxiv created 2002/04/03 · arxiv updated 2009/11/30

Abstract

We establish what we consider to be the definitive versions of Jensen's operator inequality and Jensen's trace inequality for functions defined on an interval. This is accomplished by the introduction of genuine non-commutative convex combinations of operators, as opposed to the contractions used in earlier versions of the theory. As a consequence, we no longer need to impose conditions on the interval of definition. We show how this relates to the pinching inequality of Davis, and how Jensen's trace inequlity generalizes to C*-algebras..

Cited by

• Fields of covariances on non-commutative probability spaces in finite dimensions
• Observational entropy of quantum correlations and entanglement
• On the Monotonicity of relative entropy: A Comparative Study of Petz's and Uhlmann's Approaches
• Instance-Optimal Matrix Multiplicative Weight Update and Its Quantum Applications
• Error Exponents for Quantum Packing Problems via An Operator Layer Cake Theorem

Related

• Jensen's trace inequality in several variables
• On the Operator Jensen Inequality for Convex Functions
• An extension of Jensen's operator inequality and its application to Young inequality
• A sharper bound for the Jensen's operator inequality
• Jensen operator inequality for strongly convex functions