Notes on some inequalities for Hilbert space operators (Q1109307)

The main result of this paper is the proof that \(| (Tx,y)| \leq \| f(| T|)x\| \| g(| T\) \(*|)y\|\) for all x,y in the Hilbert space H, where T is an arbitrary bounded operaor in H and f, g are nonnegative functions on [0,\(\infty)\) which are continuous and satisfying the relation \(f(t)g(t)=t\). This proof may be considered as a new proof of Heinz inequality. Other operator inequalities such as Reid inequality and Weyl inequality are considered.