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http://dx.doi.org/10.14317/jami.2022.785

LOCAL SPECTRAL THEORY AND QUASINILPOTENT OPERATORS  

YOO, JONG-KWANG (Department of Flight Operation, Chodang University)
Publication Information
Journal of applied mathematics & informatics / v.40, no.3_4, 2022 , pp. 785-794 More about this Journal
Abstract
In this paper we show that if A ∈ L(X) and R ∈ L(X) is a quasinilpotent operator commuting with A then XA(F) = XA+R(F) for all subset F ⊆ ℂ and 𝜎loc(A) = 𝜎loc(A + R). Moreover, we show that A and A + R share many common local spectral properties such as SVEP, property (C), property (𝛿), property (𝛽) and decomposability. Finally, we show that quasisimility preserves local spectrum.
Keywords
Bishop's property (${\beta}$); decomposable; decomposition property (${\delta}$); Dunford's property (C); local spectrum; quasinilpotent; quasisimilar; SVEP;
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