Bulletin of the
Korean Mathematical Society BKMS

In this paper we introduce and study the new properties $(W {\scriptstyle \Pi})$, $(UW {\scriptstyle \Pi_a})$, $(UW {\scriptstyle E})$ and $(UW {\scriptstyle \Pi}).$ The main goal of this paper is to study relationship between these new properties and other Weyl type theorems. Moreover, we reconsider several earlier results obtained respectively in \cite{BK}, \cite{RA2}, \cite{DH}, \cite{AB} and \cite{BZ1} for which we give stronger versions.

Keywords: property $(W {\scriptstyle \Pi})$, property $(UW {\scriptstyle \Pi_a})$, property $(UW {\scriptstyle \Pi})$, property $(UW {\scriptstyle E }),$ Weyl-type theorems

MSC numbers: Primary 47A53, 47A10