Spectral pictures of hyponormal bilateral operator weighted shifts
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- by Domingo A. Herrero PDF
- Proc. Amer. Math. Soc. 109 (1990), 753-763 Request permission
Abstract:
This note provides a complete description of the spectral picture of a hyponormal bilateral operator weighted shift of finite multiplicity. If the weights are $m \times m$ matrices, then the operator cannot by cyclic, unless it is a normal operator of a very special kind. An example shows that, nevertheless, there exists a cyclic, nonnormal, hyponormal bilateral operator weighted shift whose weights are operators acting on an infinite dimensional Hilbert space. (This answers a question of J. B. Conway.)References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 753-763
- MSC: Primary 47B20; Secondary 47A10, 47B37
- DOI: https://doi.org/10.1090/S0002-9939-1990-1014644-3
- MathSciNet review: 1014644