J. B. Conway and T.A. Gillespie (J. Funct. Anal. 64 (1985), 178-189) characterized those reductive normal operators which have isomorphic invariant subspace lattices. In a subsequent paper (J. Operator Theory 22 (1989), 31-49) they gave several necessary conditions of isomorphism in the class of nonreductive isometries. In this paper we provide a new necessary condition when the isometry contains a bilateral shift. Furthermore, we give complete characterization if the nonreductive components of the isometries are cyclic. It turns out that this characterization is of different types in the unitary and in the nonunitary case. We describe also when absolutely continuous unitary operators have spatially isomorphic invariant subspace lattices. Our results provide answers for questions posed in the second Conway and Gillespie paper referenced above. (C) 2000 Academic Press. [References: 15]
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机译：J.B.康威和T.A. Gillespie（J. Funct。Anal。64（1985），178-189）描述了那些具有同构不变子空间格的归约正则算子。在随后的论文中（J. Operator Theory 22（1989），31-49），他们给出了非归约对称性类中同构的几个必要条件。在本文中，当等轴测线包含双向位移时，我们提供了一个新的必要条件。此外，如果等距的非还原性成分是循环的，我们将给出完整的表征。事实证明，这种特征在单一和非单一情况下具有不同的类型。我们还描述了绝对连续unit算子何时具有空间同构不变子空间格。我们的结果为上述第二篇Conway和Gillespie论文中提出的问题提供了答案。 （C）2000学术出版社。 [参考：15]
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