Polaroid and k-quasi-∗-paranormal Operators

Abstract

An operator T is said to be k-quasi-∗-paranormal if ||Tk+2x||||Tkx|| ≥ ||T∗Tkx||2for all x ∈ H, where
k is a natural number. In this paper, we give the inclusion relation of k-quasi-∗-paranormal operators and
k-quasi-∗-A operators. And we prove that if T is an algebraically k-quasi-∗-paranormal operator, then T is
polaroid and has SVEP. We also show that if T is an algebraically k-quasi-∗-paranormal operator, then Weyl
type theorems hold for T.