Tcaciuc, Adi2024-03-192024-03-192022Tcaciuc, A. (2022). Invariant subspace problem for rank-one perturbations: the quantitative version. Journal of Functional Analysis, 283(5): 109548. https://doi.org/10.1016/j.jfa.2022.109548https://hdl.handle.net/20.500.14078/3487We show that for any bounded operator T acting on an infinite dimensional complex Banach space, and for any ε > 0, there exists an operator F of rank at most one and norm smaller than ε such that T + F has an invariant subspace of infinite dimension and codimension. A version of this result was proved in [T19] under additional spectral conditions for T or T∗. This solves in full generality the quantitative version of the invariant subspace problem for rank-one perturbations.enAttribution-NonCommercial-NoDerivs (CC BY-NC-ND)operatorinvariant subspacefinite rankperturbationArticle Post-Printhttps://doi.org/10.1016/j.jfa.2022.109548