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

Abstract

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 this paper we establish various inequalities between the operator norm and its numerical radius of $(\alpha ,\beta )$-normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.

11 pages

References in corpus (2)

• Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces
• New Reverses of Schwarz, Triangle and Bessel Inequalities in Inner Product Spaces