Polaroid and k-quasi-*-paranormal operators

Fei Zuo, Junli Shen
2016 Filomat  
An operator T is said to be k-quasi- * -paranormal if ||T k+2 x||||T k x|| ≥ ||T * T k x|| 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.
doi:10.2298/fil1602313z fatcat:5wdmikiu4zgkteh326ykbxgzvm