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New versions of reverse Young and Heinz mean inequalities with the Kantorovich constant. (English) Zbl 1357.26048

Summary: We show new versions of reverse Young inequalities by virtue of the Kantorovich constant, and utilizing the new reverse Young inequalities we give the reverses of the weighted arithmetic-geometric and geometric-harmonic mean inequalities for two positive operators. Also, new versions of reverse Young and Heinz mean inequalities for unitarily invariant norms are established.

MSC:

26D20 Other analytical inequalities
15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
26E60 Means
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
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