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

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

2007-08-13

arxiv.org/abs/0708.1657v2

Mathematics

Functional Analysis

11 pages

Scientific paper

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

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