On generalized property (v) for bounded linear operators
An operator T acting on a Banach space X has property (gw) if σa(T ) \ σ SBF− + (T ) = E(T ), where σa(T ) is the approximate point spectrum of T , σSBF− + (T ) is the upper semi-B-Weyl spectrum of T and E(T ) is the set of all isolated eigenvalues of T . We introduce and study two new spectral properties (v) and (gv) in connection with Weyl type theorems. Among other results, we show that T satisfies (gv) if and only if T satisfies (gw) and σ(T ) = σa(T ).