English

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

Functional Analysis 2008-04-30 v2 Operator Algebras

Abstract

An operator TT acting on a Hilbert space is called (α,β)(\alpha ,\beta)-normal (0α1β0\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 (α,β)(\alpha ,\beta)-normal operators in Hilbert spaces. For this purpose, we employ some classical inequalities for vectors in inner product spaces.

Keywords

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

R2 v1 2026-06-21T09:06:56.130Z