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Operator iteration on the Young inequality. (English) Zbl 1353.47014
Summary: In this paper, we employ iteration on operator version of the famous Young inequality and obtain more arithmetic-geometric mean inequalities and the reverse versions for positive operators. Concretely, we obtain refined Young inequalities with the Kantorovich constant, the reverse ratio type and difference type inequalities for arithmetic-geometric operator mean under different conditions.

MSC:
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
47A63 Linear operator inequalities
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