On Strong Variations of Weyl Type Theorems

An operator T acting on a Banach space X satisfies the property (UWE) if σa(T ) r σSF− + (T ) = E(T ), where σa(T ) is the aproximate point spectrum of T , σ SF− + (T ) is the upper semi-Weyl spectrum of T and E(T ) is the set of all eigenvalues of T that are isolated in the spectrum σ(T ) of T . In this paper, we introduce and study two new spectral properties, namely (VE) and (VEa ), in connection with Weyl type theorems. Among other results, we have that T satisfies property (VE) if and only if T satisfies property (UWE) and σ(T ) = σa(T ).