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Proceedings of the American Mathematical Society

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

 

 

Reducing decompositions for strictly cyclic operators


Author: Richard Bouldin
Journal: Proc. Amer. Math. Soc. 40 (1973), 477-481
MSC: Primary 47A15
MathSciNet review: 0320777
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Abstract: If $ T$ is a strictly cyclic operator on $ H$ then $ H$ has a direct sum decomposition $ {H_1} \oplus {H_2}$ where $ {H_1}$ and $ {H_2}$ are invariant under $ T$ if and only if the spectrum of $ T$ is not connected. If $ \lambda $ is a reducing eigenvalue for the strictly cyclic operator $ T$ then the multiplicity of $ \lambda $ is one and $ \lambda $ is an isolated point of the spectrum of $ T$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0320777-7
Article copyright: © Copyright 1973 American Mathematical Society