Numerical radius inequalities of operator matrices from a new norm on B(H)

Abstract

This paper is a continuation of a recent work on a new norm, christened the (α, β)norm, on the space of bounded linear operators on a Hilbert space. We obtain some upper bounds for the said norm of n × n operator matrices. As an application of the present study, we estimate bounds for the numerical radius and the usual operator norm of n × n operator matrices, which generalize the existing ones.