Numerical radius inequalities of operator matrices from a new norm on $\mathcal{B}(\mathcal{H})$

Abstract

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

References in corpus (1)

• On a new norm on $\mathcal{B}(\mathcal{H})$ and its applications to numerical radius inequalities

Cited by in corpus (1)

• New semi-norm of semi-Hilbertian space operators and its application