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.
"A Survey of Jensen Type Inequalities for Log-Convex Functions of Selfadjoint Operators in Hilbert Spaces." Commun. Math. Anal. 10 (1) 82 - 104, 2011.