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

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.


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