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
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