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The inaccessible invariant subspaces of certain $ C\sb{0}$ operators

Author: John Daughtry
Journal: Proc. Amer. Math. Soc. 78 (1980), 51-55
MSC: Primary 47A15; Secondary 47A20, 47A45
MathSciNet review: 548083
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Abstract: We extend the Douglas-Pearcy characterization of the inaccessible invariant subspaces of an operator on a finite-dimensional Hilbert space to the cases of algebraic operators and certain $ {C_0}$ operators on any Hilbert space. This characterization shows that the inaccessible invariant subspaces for such an operator form a lattice. In contrast to D. Herrero's recent result on hyperinvariant subspaces, we show that quasisimilar operators in the classes under consideration have isomorphic lattices of inaccessible invariant subspaces.

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Keywords: $ {C_0}$ operators, invariant subspaces, quasisimilarity
Article copyright: © Copyright 1980 American Mathematical Society

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