Browder's theorems and spectral continuity

Abstract

Let X be a complex infinite dimensional Banach space. We use σ_a(T) andσ_{ea}(T) , respectively, to denote the approximate point spectrum and the essential approximate point spectrum of a bounded operator T onX . Also, \pi _a(T) denotes the set <$>{\rm{iso} σ_a(T)\backslash σ_{ea}(T)}<$>. An operator T onX obeys the a-Browder's theorem provided that<> . We investigate connections between the Browder's theorems, the spectral mapping theorem and spectral continuity.