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Proceedings of the American Mathematical Society

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A note on reductive operators


Author: Frank Gilfeather
Journal: Proc. Amer. Math. Soc. 44 (1974), 101-105
MSC: Primary 47A15
DOI: https://doi.org/10.1090/S0002-9939-1974-0341132-0
MathSciNet review: 0341132
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Abstract: A bounded linear operator $ A$ on a Hilbert space is called reductive if every invariant subspace of $ A$ reduces it. This paper gives examples of operators which give an affirmative answer to the reductive question: If $ A$ is reductive, then is $ A$ normal?


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DOI: https://doi.org/10.1090/S0002-9939-1974-0341132-0
Keywords: Reductive operator, invariant subspace
Article copyright: © Copyright 1974 American Mathematical Society