Hypercyclicity, supercyclicity and generalized rakočević's property

A Banach space operator satisfies generalized Rakocevic's property (gw) if the complement of its upper semi B-Weyl spectrum in its approximate point spectrum is the set of eigenvalues of T which are isolated in the spectrum of T. In this note, we characterize hypecyclic and supercyclic operators satisfying the property (gw).