A Cauchy-Schwarz inequality for operators with applications Original Research Article

For any unitarily invariant norm on Hilbert-space operators it is shown that for all operators A, B, X and positive real numbers r we have A*XBr 2 less-than-or-equals, slant AA*Xr XBB*r . Some consequences are then discussed. A simple proof is given for the fact that for positive operators A, B the function [spr(AtBt)]1/t is monotone in t on the positive half line.