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On a Jensen-Mercer operator inequality. (English) Zbl 1221.47031
The Jensen-Mercer operator inequality has been proved by the authors in [Linear Algebra Appl. 418, No. 2–3, 551–564 (2006; Zbl 1105.47017)]. In the present paper, the authors obtain a general formulation of the Jensen-Mercer operator inequality. In fact, they obtain the Jensen-Mercer operator inequality for operator convex functions, for continuous fields of operators and for unital fields of positive linear mappings. Then the authors obtain an upper global bound of Jensen’s operator functional as an application of the result.
MSC:
47A63Operator inequalities
47A64Operator means, shorted operators, etc.