Translator Disclaimer
1 June 2019 The invariant subspace problem for rank-one perturbations
Adi Tcaciuc
Duke Math. J. 168(8): 1539-1550 (1 June 2019). DOI: 10.1215/00127094-2018-0071

Abstract

We show that for any bounded operator T acting on an infinite-dimensional Banach space there exists an operator F of rank at most one such that T+F has an invariant subspace of infinite dimension and codimension. We also show that whenever the boundary of the spectrum of T or T does not consist entirely of eigenvalues, we can find such rank-one perturbations that have arbitrarily small norm. When this spectral condition is not satisfied, we can still find suitable finite-rank perturbations of arbitrarily small norm, but not necessarily of rank one.

Citation

Download Citation

Adi Tcaciuc. "The invariant subspace problem for rank-one perturbations." Duke Math. J. 168 (8) 1539 - 1550, 1 June 2019. https://doi.org/10.1215/00127094-2018-0071

Information

Received: 26 September 2017; Revised: 9 December 2018; Published: 1 June 2019
First available in Project Euclid: 15 May 2019

zbMATH: 07080118
MathSciNet: MR3959865
Digital Object Identifier: 10.1215/00127094-2018-0071

Subjects:
Primary: 47A15
Secondary: 47A55

Rights: Copyright © 2019 Duke University Press

JOURNAL ARTICLE
12 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.168 • No. 8 • 1 June 2019
Back to Top