## The invariant subspace problem for rank one perturbations

2019
##### Keywords
functional analysis
##### Abstract (summary)
We 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.
##### Publication Information
Tcaciuc, A. (2019). The invariant subspace problem for rank one perturbations. Duke Mathematical Journal 168(8), 1539-1550, https://doi.org/10.1215/00127094-2018-0071
English