ON QUASI CLASS Q(N) AND
QUASI CLASS Q^*(N) OPERATORS
Valdete Rexhëbeqaj Hamiti1, Shqipe Lohaj2
1,2Faculty of Electrical and Computer Engineering
Department of Mathematics
University of Prishtina “Hasan Prishtina”
Prishtinë, 10 000, KOSOVË

Abstract

Let $T$ be a bounded linear operator on a complex Hilbert space $\mathcal{H}$. In this paper we introduce two new classes of operators: quasi class $Q(N)$ and quasi class $Q^*(N).$ An operator $T\in \mathcal{L}(\mathcal{H})$ is of quasi class $Q(N)$ for a fixed real number $N\geq 1,$ if $T$ satisfies

\begin{displaymath}N\Vert T^{2}x\Vert^{2} \leq \Vert T^3 x\Vert^{2}+ \Vert Tx\Vert^{2},\end{displaymath}

for all $x\in \mathcal{H}$. And an operator $T\in \mathcal{L}(\mathcal{H})$ is of quasi class $Q^*(N)$ for a fixed real number $N\geq 1,$ if $T$ satisfies

\begin{displaymath}N\Vert T^*Tx\Vert^{2} \leq \Vert T^3 x\Vert^{2}+ \Vert Tx\Vert^{2},\end{displaymath}

for all $x\in \mathcal{H}.$ We study basic properties of these classes of operators, the structural and spectral properties, a matrix representation and also the Aluthge transformation.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 32
Issue: 3
Year: 2019

DOI: 10.12732/ijam.v32i3.10

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