Weak forms of supercyclity and a class of paranormal operators

In this paper, we give several properties of class A operators, an interesting subclass of paranormal operators. In particular, we consider the operators TL(H ) such that T -? is a class A operator for every C. We also provide some cases for class A operators to have a nontrivial invariant subspace. Finally, we prove that there are no N -supercyclic class A operators with trivial kernel for any positive integer N and that weakly supercyclic class A operators with trivial kernel must be normal.