Almost invariant half-spaces of operators on Banach spaces

2009/01/07 by Androulakis, George, Popov, Alexey I., Tcaciuc, Adi +1 · 1 citation
#47A15 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.0901.0752

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 ≤ p < ∞) or c₀.

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