On the Hyponormal Property of Operators

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Let $T$ be a bounded linear operator on a Hilbert space $mathscr{H}$. We say that $T$ has the hyponormal property if there exists a function $f$, continuous on an appropriate set so that $f(|T|)geq f(|T^ast|)$. We investigate the properties of such operators considering certain classes of functions on which our definition is constructed. For such a function $f$ we introduce the $f$-Aluthge transform, $tilde{T}_{f}$. Given two continuous functions $f$ and $g$ with the property  $f(t)g(t)=t$, we also introduce the $(f,g)$-Aluthge transform, $tilde{T}_{(f,g)}$. The features of these transforms are discussed as well.

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:15 Issue: 2, Nov 2020
Pages:
21 to 30
https://www.magiran.com/p2194658