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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.

MSC:

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