Tcaciuc, Adi2020-12-162022-05-312022-05-312019Tcaciuc, 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.2019.04.026https://hdl.handle.net/20.500.14078/2102We 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.415.84KBPDFenAll Rights Reservedhttps://doi.org/10.1016/j.jmaa.2019.04.026