Some inequalities for $(α, β)$-normal operators in Hilbert spaces

Dragomir, Sever S.; Moslehian, Mohammad Sal

Some inequalities for $(α, β)$-normal operators in Hilbert spaces

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Description

An operator $T$ acting on a Hilbert space is called $(α,β)$-normal ($0\leq α\leq 1\leq β$) 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 $(α,β)$-normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.
11 pages