Almost invariant half-spaces of algebras of operators

Details Almost invariant half-spaces of algebras of operators Almost invariant half-spaces of algebras of operators

2009-09-18

arxiv.org/abs/0909.3491v1

Mathematics

Functional Analysis

14 pages

Scientific paper

Given a Banach space X and a bounded linear operator T on X, a subspace Y of X is almost invariant under T if TY is a subspace of Y+F for some finite-dimensional ``error'' F. In this paper, we study subspaces that are almost invariant under every operator in an algebra A of operators acting on X. We show that if A is norm closed then the dimensions of ``errors'' corresponding to operators in A must be uniformly bounded. Also, if A is generated by a finite number of commuting operators and has an almost invariant half-space (that is, a subspace with both infinite dimension and infinite codimension) then A has an invariant half-space.

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