Kadison’s Schwarz and Kantorovich inequalities on correlation operators

Applying Kadison’s Schwarz inequality and the Kantorovich inequality to Hadamard products of operators, we show some facts on correlation operators which are defined in virture of the Hadamard product

Weakly selfadjoint operators

Extending the notion of a weakly positive operator introduced by Wigner, we define a weakly selfadjoint operator as the product of two selfadjoint operators, one of whose factors is positive, and show some facts on the operator

Some extensions of Grüss’ inequality

We give some extensions of Grüss’ inequalities of discrete and integral types, which refine or generalize recent results due to P. Cerone and S. S. Dragomir and those due to some other authors