Korean J. Math. Vol. 23 No. 2 (2015) pp.249-257
DOI: https://doi.org/10.11568/kjm.2015.23.2.249

Structural and spectral properties of $k$-quasi-$*$-paranormal operators

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Published: Jun 30, 2015
Keywords:
k-quasi-∗-paranormal operator, spectral continuity, joint approximate point spectrum.
Mathematics Subject Classification:
k-quasi-∗-paranormal operator, 47B20, 47A10.

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Fei Zuo
College of Mathematics and Information Science Henan Normal University Xinxiang 453007, People’s Republic of China
Hongliang Zuo
College of Mathematics and Information Science Henan Normal University Xinxiang 453007, People’s Republic of China

Abstract

For a positive integer $k$, an operator $T$ is said to be $k$-quasi-$*$-paranormal if $||T^{k+2}x||||T^{k}x||\geq||T^{*}T^{k}x||^{2}$ for all $x\in H$, which is a generalization of $*$-paranormal operator. In this paper, we give a necessary and sufficient condition for $T$ to be a $k$-quasi-$*$-paranormal operator. We also prove that the spectrum is continuous on the class of all $k$-quasi-$*$-paranormal operators.


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Supporting Agencies

This work is supported by the Natural Science Foundation of the Depart- ment of Education of Henan Province (No.14B110008 No.14B110009) the Basic Science and Technological Frontier Project of Henan Province(No.132300410261 No.142300410167).

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