Spectral pictures of hyponormal bilateral operator weighted shifts

Herrero, Domingo A.

doi:10.1090/S0002-9939-1990-1014644-3

Spectral pictures of hyponormal bilateral operator weighted shifts
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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.)

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