MATEMATIQKI VESNIK PROPERTY (gz) FOR BOUNDED LINEAR OPERATORS

H Zariouh
unpublished
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 Ea(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
more » ... 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 SBF − + (T) is the essential semi-B-Fredholm spectrum of T .
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