A note on the \(a\)-Browder’s and \(a\)-Weyl’s theorems. (English) Zbl 1199.47067

Amouch, M.; Zguitti, H.

Math. Bohem. 133, No. 2, 157-166 (2008).

Summary: Let \(T\) be a Banach space operator. In this paper, we characterize \(a\)-Browder’s theorem for \(T\) by the localized single valued extension property. Also, we characterize \(a\)-Weyl’s theorem under the condition \(E^a(T)=\pi ^a(T),\) where \(E^a(T)\) is the set of all eigenvalues of \(T\) which are isolated in the approximate point spectrum and \(\pi ^a(T)\) is the set of all left poles of \(T\). Some applications are also given.

MSC:

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

Keywords:

B-Fredholm operator; Weyl’s theorem; operator of Kato type; single-valued extension property (SVEP)