Extension of Jensen’s inequality for operators without operator convexity. (English) Zbl 1221.47032

Summary: We give an extension of Jensen’s inequality for \(n\)-tuples of selfadjoint operators, unital \(n\)-tuples of positive linear mappings, and real-valued continuous convex functions with conditions on the operators’ bounds. We also study operator quasiarithmetic means under the same conditions.


47A63 Linear operator inequalities
47A64 Operator means involving linear operators, shorted linear operators, etc.
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