The k-quasi-∗-class contractions have property PF

Abstract

First, we will see that if T is a contraction of the k-quasi- * -class A operator, then theconverges strongly to a projection P and TT * k P = 0. Second, it will be proved that if T is a contraction of the k-quasi- * -class A operator, then either T has a non-trivial invariant subspace or T is a proper contraction. Finally it will be proved that if T belongs to the k-quasi- * -class A and is a contraction, then T has a Wold-type decomposition and T has the PF property. MSC: 47A10; 47B37; 15A18