November 2023 A Note on the Quasi-Normality of Linear Operators
Anas A. Hijab, Laith K. Shaakir, Elaf S. Abdulwahid
Missouri J. Math. Sci. 35(2): 177-187 (November 2023). DOI: 10.35834/2023/3502177

Abstract

In this paper, we introduce the quasi-normality set, denoted by $ E_A $, which is a strong extension of the normality set, denoted by $ N_A$ for any operator $A$ in the Banach algebra $\mathcal{B(H)}$. Furthermore, we show some interesting properties and remarkable results with the Unilateral Weighted shift and Volterra operators. Finally, we show that a quasi-normality set is no invariant and has an invariant subspace for some transpose linear operators.

Citation

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Anas A. Hijab. Laith K. Shaakir. Elaf S. Abdulwahid. "A Note on the Quasi-Normality of Linear Operators." Missouri J. Math. Sci. 35 (2) 177 - 187, November 2023. https://doi.org/10.35834/2023/3502177

Information

Published: November 2023
First available in Project Euclid: 28 November 2023

Digital Object Identifier: 10.35834/2023/3502177

Subjects:
Primary: 47B15
Secondary: 15A16 , 47A15 , 47B25

Keywords: $E$-self adjoint , invariant subspace , normality set , quasi-normality set , similar operator

Rights: Copyright © 2023 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.35 • No. 2 • Nov 2023
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