The invariant subspace problem for rank one perturbations
The invariant subspace problem for rank one perturbations
Author
Tcaciuc, Adi
Faculty Advisor
Date
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
DOI
Notes
Item Type
Language
English
Rights
All Rights Reserved