Jensen's Operator Inequality

By Frank Hansen, G. Pedersen. 2002

219 citations recorded by the source corpus.

Jensen's operator inequality and Jensen's trace inequality for real functions defined on an interval are established in what might be called their definitive versions. This is accomplished by the introduction of genuine non‐commutative convex combinations of operators, as opposed to the contractions considered in earlier versions of the theory by the authors, and by Brown and Kosaki. As a consequence, one no longer needs to impose conditions on the interval of definition. It is shown how this relates to the pinching inequality of Davis, and how Jensen's trace inequality generalizes to C*‐algebras. 2000 Mathematics Subject Classification 47A56 (primary), 46L10, 47C15, 26A51 (secondary).

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a29f2354cbc92ebfae45c27106108f557decf5fb

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Unitary orbits of Hermitian operators with convex or concave functions (2011, background): “5) is due to Hansen–Pedersen [20], and the special case (2.”
User-Friendly Tail Bounds for Sums of Random Matrices (2010, background): “13) Every operator convex function admits an operator Jensen’s inequality [25].”
A Fully Quantum Asymptotic Equipartition Property (2008, background): “A generalization of Jensen’s inequality to operator convex functions is given in [23].”
Noncommutative Choquet Theory (2019, unknown): “We obtain a noncommutative analogue of Jensen’s inequality that specializes in this case to the Hansen-Pedersen-Jensen inequality [33].”