Some inequalities for $(\alpha ,\beta )$-normal operators in Hilbert spaces

Sever S. Dragomir, Mohammad Sal Moslehian

An operator $T$ acting on a Hilbert space is called $(\alpha ,\beta )$-normal ($0\le \alpha \le 1\le \beta$) if \begin{equation*} α^{2}T^{\ast }T\leq TT^{\ast}\leq β^{2}T^{\ast}T. \end{equation*} In…