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

Fei Zuo, Hongliang Zuo

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.

Keywords


k-quasi-∗-paranormal operator, spectral continuity, joint approximate point spectrum.

Subject classification

47B20, 47A10.

Sponsor(s)

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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