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Czechoslovak Mathematical Journal
In this paper, by the definition of Berezin number, we present some inequalities involving the operator geometric mean. For instance, it is shown that if X, Y, Z ∈ L(H) such that X and Y are positive operators, then in which X Y = X 1 2 (X -1 2 YX -1 2 ) 1 2 X 1 2 , p ≥ q > 1 such that r ≥ 2 q and 1 p + 1 q = 1. MSC: Primary 47A63; secondary 15A60doi:10.21136/cmj.2018.0048-17 fatcat:fd3hnnrci5dhxfl7syms5egaa4