For a positive integer k, an operator T is said to be k-quasi-*-paranormal if ${\parallel}T^{k+2}x{\parallel}{\parallel}T^kx{\parallel}{\geq}{\parallel}T^*T^kx{\parallel}^2$ for all x $\in$ H, which is a generalization of *-paranormal operator. In thi...
For a positive integer k, an operator T is said to be k-quasi-*-paranormal if ${\parallel}T^{k+2}x{\parallel}{\parallel}T^kx{\parallel}{\geq}{\parallel}T^*T^kx{\parallel}^2$ 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.