Variations of Weyl type theorems

Abstract

‎A Banach space operator $T$ satisfies property($Bgw$)‎, ‎a variant‎ ‎property$(gw)$‎, ‎if the complement in the approximate point spectrum‎ ‎$\sigma_{a}(T)$ of the semi-B-essential approximate point spectrum‎ ‎$\sigma_{SBF^{-}_{+}}(T)$ coincides with set of isolated eigenvalues‎ ‎of $T$ of finite multiplicity $E^{0}(T)$‎. ‎We also introduce‎ ‎properties $(Bb)$‎, ‎and property $(Bgb)$ in connection with Weyl type‎ ‎theorems‎, ‎which are analogous‎, ‎respectively‎, ‎to generalized‎ ‎Browder's theorem and property($gb$)‎. ‎We obtain relation among‎ ‎these new properties‎.