Spectral properties, contractions and Fuglede-Putnam theorem for A*_n operator

Abstract

In this paper, we introduce a new class of operators, called class A ∗ operators, which a superclass of hyponormal operators and a subclass of n −∗ −paranormal operators. We will show spectral properties of this class of operators. Next, it will be proved that if T is a contraction of A ∗ class operators, then either T has a nontrivial invariant subspace or T is a proper contraction, and the nonnegative operator D = |T n+1 | 2 n+1 −| T ∗ | 2 is a strongly stable contraction. Further, we prove Fuglede-Putnam theorem for class A ∗ operator.