Some inequalities for $(\alpha, \beta)$-normal operators in Hilbert spaces
Functional Analysis
2008-04-30 v2 Operator Algebras
Abstract
An operator acting on a Hilbert space is called -normal () 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 -normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.
Cite
@article{arxiv.0708.1657,
title = {Some inequalities for $(\alpha, \beta)$-normal operators in Hilbert spaces},
author = {Sever S. Dragomir and Mohammad Sal Moslehian},
journal= {arXiv preprint arXiv:0708.1657},
year = {2008}
}
Comments
11 pages