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An operator $T$ acting on a Banach space $X$ possesses property $\left(\mathrm{gw}\right)$ if ${\sigma }_a\left(T\right)\setminus {\sigma }_{{\mathrm{SBF}}_{+}^{-}}\left(T\right)=E\left(T\right),$ where ${\sigma }_a\left(T\right)$ is the approximate point spectrum of $T$, ${\sigma }_{{\mathrm{SBF}}_{+}^{-}}\left(T\right)$ is the essential semi-B-Fredholm spectrum of $T$ and $E\left(T\right)$ is the set of all isolated eigenvalues of $T.$ In this paper we introduce and study two new properties $\left(\mathrm{b}\right)$ and $\left(\mathrm{gb}\right)$ 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...