A bounded linear operator T acting on a Banach space possesses property (gaw) if σ(T ) E a (T ) = σ BW (T ), where σ BW (T ) is the B-Weyl spectrum of T , σ(T ) is the usual spectrum of T and E a (T ) is the set of all eigenvalues of T which are isolated in the approximate point spectrum of T . In this paper we introduce and study the new spectral properties (z), (gz), (az) and (gaz) as a continuation of [M. Berkani, H. Zariouh, New extended Weyl type theorems, Mat. Vesnik 62 (2010), 145–154], which are related to Weyl type theorems. Among other results, we prove that T possesses property (gz) if and only if T possesses property (gaw) and σ BW (T ) = σ SBF . + (T ); where σ SB F . + (T ) is the essential semi-B-Fredholm spectrum of T .
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