Almost invariant half-spaces of operators on Banach spaces

Androulakis, George; Popov, Alexey I.; Tcaciuc, Adi; Troitsky, Vladimir G.

Almost invariant half-spaces of operators on Banach spaces

Authors

Androulakis, George

Popov, Alexey I.

Tcaciuc, Adi

Troitsky, Vladimir G.

Description

We introduce and study the following modified version of the Invariant Subspace Problem: whether every operator T on a Banach space has an almost invariant half-space, that is, a subspace Y of infinite dimension and infinite codimension such that Y is of finite codimension in T(Y). We solve this problem in the affirmative for a large class of operators which includes quasinilpotent weighted shift operators on l_p (1 \le p < \infty) or c_0.
13 pages