Spectral cutting for a class of subnormal operators
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- by Bhushan L. Wadhwa PDF
- Proc. Amer. Math. Soc. 97 (1986), 281-285 Request permission
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 ${T^ * }|{M^ * }$ contained in the conjugate of the boundary of $\delta$. The minimal normal extension of the subnormal operator $T|M(\delta )$ is also considered.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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