Almost invariant half-spaces of operators on Banach spaces

Details Almost invariant half-spaces of operators on Banach spaces Almost invariant half-spaces of operators on Banach spaces

2009-01-07

arxiv.org/abs/0901.0752v1

Mathematics

Functional Analysis

13 pages

Scientific paper

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.

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