Some results about spectral continuity and compact perturbations

Abstract

In this paper, we are interested in the continuity of the spectrum and some of its parts in the setting of Hilbert spaces. We study a particular case of continuity of the spectrum in the operator class of the type {T} + K(H), where K(H) denote the ideal of compact operators. Also, we give conditions in order to transfer the continuity of spectrum from T to T + K, where K ∈ K(H). Then, we characterize those operators for which the continuity of spectrum is stable under compact perturbations.