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A Survey of Jensen Type Inequalities for Log-Convex Functions of Selfadjoint Operators in Hilbert Spaces

Commun. Math. Anal.
Volume 10, Number 1 (2011), 82 - 104

A Survey of Jensen Type Inequalities for Log-Convex Functions of Selfadjoint Operators in Hilbert Spaces

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Abstract

Some recent Jensen's type inequalities for log-convex functions of selfadjoint operators in Hilbert spaces under suitable assumptions for the involved operators are surveyed. Applications in relation with some celebrated results due to Hölder-McCarthy and Ky Fan are provided as well.