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Proceedings of the American Mathematical Society

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

 

 

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 $ A = {A_1} \oplus {A_2}$, where $ {A_1}$ is normal and all the invariant subspaces of $ {A_2}$ 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 $ AT = TA$, then $ {A^ \ast }T = T{A^ \ast }$. 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