LATTICES OF INVARIANT SUBSPACES FOR A QUASIAFFINE TRANSFORM OF A UNILATERAL SHIFT OF FINITE MULTIPLICITY

摘要

Let T be a contraction, let S be a unilateral shift of finite multiplicity, and let X be an operator with zero kernel, dense range, and such that XT = SX. Then the mapping E |→ clos XE, E ∈ Lat T, is an isomorphism between the lattices Lat T and Lai S of invariant subspaces of T and S. Bibliography: 8 titles.