Hilbert-Schmidt Numerical Radius of a Pair of Operators.

We introduce a new norm on C 2 × C 2 , where C 2 is the Hilbert-Schmidt class. We study basic properties of this norm and prove inequalities involving it. As an application of the present study, we deduce a chain of new bounds for the Hilbert-Schmidt numerical radii of 2 × 2 operator matrices. Connection with the classical Hilbert-Schmidt numerical radius of a single operator are also provided. Moreover, we refine some related existing bounds, too. [ABSTRACT FROM AUTHOR]