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Jensen's Operator Inequality
Author(s) -
Hansen Frank,
Pedersen Gert K.
Publication year - 2003
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609303002200
Subject(s) - mathematics , jensen's inequality , mathematics subject classification , inequality , kantorovich inequality , trace (psycholinguistics) , pure mathematics , log sum inequality , convex function , regular polygon , operator (biology) , rearrangement inequality , commutative property , interval (graph theory) , algebra over a field , calculus (dental) , combinatorics , linear inequality , mathematical analysis , convex analysis , convex optimization , linguistics , geometry , philosophy , dentistry , repressor , chemistry , biochemistry , transcription factor , medicine , gene
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).