Hyperinvariant subspaces of reductive operators

Author:
Robert L. Moore

Journal:
Proc. Amer. Math. Soc. **63** (1977), 91-94

MSC:
Primary 47A15

MathSciNet review:
0435888

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Abstract: T. B. Hoover has shown that if *A* is a reductive operator, then , where is normal and all the invariant subspaces of are hyperinvariant. A new proof is presented of this result, and several corollaries are derived. Among these is the fact that if *A* is hyperinvariant and *T* is polynomially compact and , then . It is also shown that every reductive operator is quasitriangular.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1977-0435888-9

Keywords:
Reductive operator,
hyperreducing subspace,
hyporeductive operator

Article copyright:
© Copyright 1977
American Mathematical Society