Some Berezin number inequalities for operator matrices
english

Mojtaba Bakherad
2018 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 15A60
doi:10.21136/cmj.2018.0048-17 fatcat:fd3hnnrci5dhxfl7syms5egaa4