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Abstract: Given a Banach space X and a bounded linear operator T on X, a subspace Y ofX is almost invariant under T if TY is a subspace of Y+F for somefinite-dimensional ``error- F. In this paper, we study subspaces that arealmost 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 isgenerated by a finite number of commuting operators and has an almost invarianthalf-space that is, a subspace with both infinite dimension and infinitecodimension then A has an invariant half-space.



Author: Alexey I. Popov

Source: https://arxiv.org/



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