Volume 15, Issue 2 (10-2020)                   IJMSI 2020, 15(2): 21-30 | Back to browse issues page

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Nabavi Sales S M S. On the Hyponormal Property of Operators. IJMSI 2020; 15 (2) :21-30
URL: http://ijmsi.ir/article-1-1088-en.html

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.

Type of Study: Research paper | Subject: General

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