| Abstrakt: |
Abstract: An operator $T$ acting on a Banach space $X$ possesses property $(\gw)$ if $\sigma_a(T)\setminus\sigma_{\SBF_+^-}(T)= E(T), $ where $\sigma_a(T)$ is the approximate point spectrum of $T$, $\sigma_{\SBF_+^-}(T)$ is the essential semi-B-Fredholm spectrum of $T$ and $E(T)$ is the set of all isolated eigenvalues of $T.$ In this paper we introduce and study two new properties $(\b)$ and $(\gb)$ in connection with Weyl type theorems, which are analogous respectively to Browder's theorem and generalized Browder's theorem. Among other, we prove that if $T$ is a bounded linear operator acting on a Banach space $X$, then property $(\gw)$ holds for $T$ if and only if property $(\gb)$ holds for $T$ and $E(T)=\Pi(T),$ where $\Pi(T)$ is the set of all poles of the resolvent of $T. |
