2002/04/03 by Frank Hansen, FRANK HANSEN, Gert K. Pedersen +1 · 12 citations
Mathematics · #Advanced Operator Algebra Research #Holomorphic and Operator Theory #Mathematical Inequalities and Applications #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 · openalex publication_date 2003/06/09 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
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).