This is an announcement for the paper "Almost invariant half-spaces of operators on Banach spaces" by George Androulakis, Alexey I. Popov, Adi Tcaciuc and Vladimir G. Troitsky. Abstract: 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. Archive classification: math.FA Mathematics Subject Classification: 47A15 Remarks: 13 pages The source file(s), invariantV9.tex: 38986 bytes, is(are) stored in gzipped form as 0901.0752.gz with size 12kb. The corresponding postcript file has gzipped size 95kb. Submitted from: vtroitsky@math.ualberta.ca The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0901.0752 or http://arXiv.org/abs/0901.0752 or by email in unzipped form by transmitting an empty message with subject line uget 0901.0752 or in gzipped form by using subject line get 0901.0752 to: math@arXiv.org.