Weyl type-theorems for direct sums. (English) Zbl 1263.47016

Berkani, Mohammed; Zariouh, Hassan

Bull. Korean Math. Soc. 49, No. 5, 1027-1040 (2012).

Weyl examined the spectra of all compact perturbations of a Hermitian operator on a Hilbert space and proved that their intersection coincides with the set of isolated points of the spectrum which are eigenvalues of finite multiplicity. Weyl’s theorem and its variants have been extended to several classes of Hilbert or Banach spaces operators. The aim of this paper is to study the behaviour of Weyl-type theorems and related notions with respect to the operation of taking orthogonal direct sums. Generalized Browder-type theorems are also discussed.

Reviewer: Cătălin Badea (Villeneuve d’Ascq)

MSC:

47A53	(Semi-) Fredholm operators; index theories
47A10	Spectrum, resolvent

Keywords:

Weyl-type theorems; Weyl spectrum; semi-Fredholm operators; Browder spectrum; property \((gb)\); property \((b)\); property \((gw)\); direct sums; essential semi-B-Fredholm spectrum