More on ( α , β ) -Normal Operators in Hilbert Spaces

Abstract

We study some properties of $(\alpha ,\beta )$-normal operators and we present various inequalities between the operator norm and the numerical radius of $(\alpha ,\beta )$-normal operators on Banach algebra ℬ($\mathscr{H}$) of all bounded linear operators $T:\mathscr{H}\to \mathscr{H}$, where $\mathscr{H}$ is Hilbert space.