Invariant subspace problem for rank-one perturbations: the quantitative version
| dc.contributor.author | Tcaciuc, Adi | |
| dc.date.accessioned | 2024-03-19T16:56:13Z | |
| dc.date.available | 2024-03-19T16:56:13Z | |
| dc.date.issued | 2022 | |
| dc.description.abstract | We 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. | |
| dc.identifier.citation | Tcaciuc, 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.2022.109548 | |
| dc.identifier.doi | https://doi.org/10.1016/j.jfa.2022.109548 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14078/3487 | |
| dc.language.iso | en | |
| dc.rights | Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) | |
| dc.rights.uri | https://creativecommons.org/licenses/by-nc-nd/4.0/ | |
| dc.subject | operator | |
| dc.subject | invariant subspace | |
| dc.subject | finite rank | |
| dc.subject | perturbation | |
| dc.title | Invariant subspace problem for rank-one perturbations: the quantitative version | en |
| dc.type | Article Post-Print |
Files
Original bundle
1 - 1 of 1
Loading...
- Name:
- Tcaciuc-Invariant-subspace-problem.pdf
- Size:
- 410.17 KB
- Format:
- Adobe Portable Document Format