Variations on a-Browder-type theorems. (English) Zbl 06315237

Berkani, M.; Kachad, M.; Zariouh, H.; Zguitti, H.

Sarajevo J. Math. 9(22), No. 2, 271-281 (2013).

Summary: We introduce and we study the new spectral properties \((SBw)\), \((SBaw)\), \((SBab)\) and \((SBb)\). Among other results, we show that if \(T\) is a bounded linear operator acting on a Banach space \(X\), then \(T\) possesses property \((SBb)\) if and only if \(T\) possesses property \((b)\) and \(\prod^0 (T) = \prod_a (T)\).

MSC:

47A53	(Semi-) Fredholm operators; index theories
47A10	Spectrum, resolvent
47A11	Local spectral properties of linear operators

Keywords:

essential semi-B-Fredholm spectrum; a-Weyl’s theorem; a-Browder’s theorem; property \((SBw)\)