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arXiv · 2006.11954

Invariant subspace problem for rank-one perturbations: the quantitative version

Adi Tcaciuc
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Abstract

We show that for any bounded operator $T$ acting on infinite dimensional, complex Banach space, and for any $\varepsilon>0$, there exists an operator $F$ of rank at most one and norm smaller than $\varepsilon$ 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.

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Adi Tcaciuc. 2020-06-22. Invariant subspace problem for rank-one perturbations: the quantitative version. https://arxiv.org/abs/2006.11954

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