Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Spectral pictures of hyponormal bilateral operator weighted shifts


Author: Domingo A. Herrero
Journal: Proc. Amer. Math. Soc. 109 (1990), 753-763
MSC: Primary 47B20; Secondary 47A10, 47B37
MathSciNet review: 1014644
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 47B20, 47A10, 47B37

Retrieve articles in all journals with MSC: 47B20, 47A10, 47B37


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1990-1014644-3
Keywords: Bilateral operator weighted shift, hyponormal operator, spectral picture, multiplicity, cyclic operator
Article copyright: © Copyright 1990 American Mathematical Society