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Polaroid and k-quasi-*-paranormal operators

Zuo Fei (Henan Normal University, College of Mathematics and Information Science, Xinxiang, China)
Shen Junli (Inner Mongolia University, School of Mathematical Sciences, Hohhot, China)

An operator T is said to be k-quasi--paranormal if ||Tk+2x||||Tkx|| ≥ ||T*Tkx||2 for 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 a polynomially k-quasi-*-paranormal operator, then T is polaroid and has SVEP. We also show that if T is a polynomially k-quasi-*-paranormal operator, then Weyl type theorems hold for T.

Keywords: Weyl’s theorem, Polaroid, k-quasi-*-paranormal operators