[Banach] Abstract of a paper by Adi Tcaciuc

This is an announcement for the paper “The almost-invariant subspace problem for Banach spaces” by Adi Tcaciuchttps://arxiv.org/find/math/1/au:+Tcaciuc_A/0/1/0/all/0/1.

Abstract: We show that for any bounded operator $T$ acting on an infinite dimensional Banach space there exists a rank one operator $F$ such that $T+F$ has invariant subspace of infinite dimension and codimension. This extends to arbitrary Banach spaces a previous result that was proved only in the reflexive case. We also show that, for any fixed $\epsilon>0$, there exists $F$ as above such that $|F|<\epsilon$.

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1707.07836