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Spectral cutting for a class of subnormal operators


Author: Bhushan L. Wadhwa
Journal: Proc. Amer. Math. Soc. 97 (1986), 281-285
MSC: Primary 47B20; Secondary 47B40
DOI: https://doi.org/10.1090/S0002-9939-1986-0835881-3
MathSciNet review: 835881
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Abstract: Let $ S$ be a subnormal decomposable operator on a Hilbert space $ \mathcal{H}$. (The dual of the Bergman shift belongs to this class.) It is shown that for any closed set $ \delta $ with nonempty intersection with the spectrum of $ S,\mathcal{H}$ can be decomposed as $ M(\delta ) \oplus \overline {M(\delta ')} \oplus {M^ * }$, where $ M(\delta )$ and $ \overline {M(\delta ')} $ are hyperinvariant under $ T$, and $ {M^ * }$ is invariant under $ {T^ * }$ with spectrum of $ {T^ * }\vert{M^ * }$ contained in the conjugate of the boundary of $ \delta $. The minimal normal extension of the subnormal operator $ T\vert M(\delta )$ is also considered.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0835881-3
Keywords: Subnormal operator, decomposable operators, Bergman shift, the minimal normal extension
Article copyright: © Copyright 1986 American Mathematical Society

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