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November 2018 A Note on Class $Q(N)$ Operators
Shqipe Lohaj, Valdete Rexhëbeqaj Hamiti
Missouri J. Math. Sci. 30(2): 185-196 (November 2018). DOI: 10.35834/mjms/1544151695

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: class $Q(N)$ and class $Q^*(N)$. An operator $T\in \mathcal{L}(\mathcal{H})$ is of class $Q(N)$ for a fixed real number $N\geq 1$, if $T$ satisfies $N\|Tx\|^{2} \leq \| T^2 x\|^{2}+ \| x\|^{2}$ for all $x\in \mathcal{H}$. And an operator $T\in \mathcal{L}(\mathcal{H})$ is of class $Q^*(N)$ for a fixed real number $N\geq 1$, if $T$ satisfies $N\|T^*x\|^{2} \leq \| T^2 x\|^{2}+ \| x\|^{2}$ for all $x\in \mathcal{H}$. We prove the basic properties of these classes of operators.

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Shqipe Lohaj. Valdete Rexhëbeqaj Hamiti. "A Note on Class $Q(N)$ Operators." Missouri J. Math. Sci. 30 (2) 185 - 196, November 2018. https://doi.org/10.35834/mjms/1544151695

Information

Published: November 2018
First available in Project Euclid: 7 December 2018

zbMATH: 06741615
MathSciNet: MR3884740
Digital Object Identifier: 10.35834/mjms/1544151695

Subjects:
Primary: 47B20

Rights: Copyright © 2018 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.30 • No. 2 • November 2018
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