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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1980-0548083-X
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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DOI: https://doi.org/10.1090/S0002-9939-1980-0548083-X
Keywords: $ {C_0}$ operators, invariant subspaces, quasisimilarity
Article copyright: © Copyright 1980 American Mathematical Society

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