科研之友
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摘要
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 subset 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 u of operators acting on X. We show that if u is norm closed then the dimensions of "errors" corresponding to operators in u must be uniformly bounded. Also, if u 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 u has an invariant half-space.
- 出版日期2010-6
