The Berkani's property and a note on some recent results

Abstract

In this paper, we continue the study of property $(U{W}_{\Pi })$ introduced in \cite{berkani2}, in connection with other Weyl type theorems. Moreover, we give counterexamples to show that some recent results related to this property, which are announced and proved by P. Aiena and M. Kachad in \cite{aiena1} are false. Furthermore, we specify the mistakes committed in each of them and we give the correct versions. We also give a global note on the paper \cite{jayanthi}.