Tcaciuc, Adi2020-12-162022-05-312022-05-312019Tcaciuc, A. (2019). The invariant subspace problem for rank one perturbations. Duke Mathematical Journal 168(8), 1539-1550, https://doi.org/10.1215/00127094-2018-0071https://hdl.handle.net/20.500.14078/2101We show that for any bounded operator T acting on 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 \cite{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.440.94KBPDFenAll Rights Reservedfunctional analysisArticle Post-Printhttps://doi.org/10.1215/00127094-2018-0071