Open AccessSome results about spectral continuity and compact perturbations
Author(s) -
Salvador Sánchez-Perales,
Slaviša V. Djordjević,
Sergio Palafox
Publication year - 2020
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2014837s
Subject(s) - mathematics , spectrum (functional analysis) , hilbert space , class (philosophy) , pure mathematics , order (exchange) , compact operator on hilbert space , mathematical analysis , compact operator , discrete mathematics , extension (predicate logic) , quantum mechanics , physics , finance , artificial intelligence , computer science , economics , programming language
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 the continuity of the spectrum in the class of operators {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.