Extended Weyl-type theorems for direct sums. (English) Zbl 1318.47019

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

Demonstr. Math. 47, No. 2, 411-422 (2014).

In this paper, the authors study the stability of extended Weyl and Browder type theorems for the orthogonal direct sum \(S\bigoplus T\), where \(S\) and \(T\) are bounded linear operators acting on a Banach space. The authors characterize the preservation of generalized a-Browder’s theorem and the property \((ab)\) under the direct sum \(S\bigoplus T\). Furthermore, some recent results are improved by removing certain superfluous assumptions.

Reviewer: Carlos R. Carpintero (Cumaná)

MSC:

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

Keywords:

generalized a-Browder’s theorem; property (\(gab\)); Weyl type theorems; direct sums; property (\(gaw\)); B-Weyl spectrum

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