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On quasinilpotent operators and the invariant subspace problem

dc.contributor.authorTcaciuc, Adi
dc.date.accessioned2020-12-16
dc.date.accessioned2022-05-31T01:43:00Z
dc.date.available2022-05-31T01:43:00Z
dc.date.issued2019
dc.description.abstractWe show that a bounded quasinilpotent operator T acting on an infinite dimensional Banach space has an invariant subspace if and only if there exists a rank one operator F and a scalar α∈ℂ, α≠0, α≠1, such that T+F and T+αF are also quasinilpotent. We also prove that for any fixed rank-one operator F, almost all perturbations T+αF have invariant subspaces of infinite dimension and codimension.
dc.format.extent415.84KB
dc.format.mimetypePDF
dc.identifier.citationTcaciuc, A. (2019). On quasinilpotent operators and the invariant subspace problem. Journal of Mathematical Analysis and Applications 477(1), 187-195. https://doi.org/10.1016/j.jmaa.2019.04.026
dc.identifier.doihttps://doi.org/10.1016/j.jmaa.2019.04.026
dc.identifier.urihttps://hdl.handle.net/20.500.14078/2102
dc.languageEnglish
dc.language.isoen
dc.rightsAll Rights Reserved
dc.titleOn quasinilpotent operators and the invariant subspace problemen

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