STRUCTURAL AND SPECTRAL PROPERTIES OF k-QUASI-*-PARANORMAL OPERATORS

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.