Geodesic
Some Inequalities of Hermite-Hadamard Typefor Convex Functions of Commuting Selfadjoint Operators
Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 491-511.

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Some operator inequalities for convex functions of commuting selfadjoint operators that are related to the Hermite-Hadamard inequality are given. Natural examples for some fundamental convex functions are presented as well. 
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Dragomir, Sever Silvestru. Some Inequalities of Hermite-Hadamard Typefor Convex Functions of Commuting Selfadjoint Operators. Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 491-511. http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a0/

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