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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On wandering vector multipliers for unitary groups


Authors: Guoxing Ji and Kichi-Suke Saito
Journal: Proc. Amer. Math. Soc. 133 (2005), 3263-3269
MSC (2000): Primary 46L10, 46L51
Published electronically: May 2, 2005
MathSciNet review: 2161148
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Abstract: A wandering vector multiplier is a unitary operator which maps the set of wandering vectors for a unitary system acting on a separable Hilbert space $\mathcal H$ into itself. It is proved that the wandering vector multipliers for a unitary group form a group, which gives a positive answer for a problem of Han and Larson. Furthermore, non-abelian unitary groups of order 6 are considered. We prove that the wandering vector multipliers of such a unitary group can not generate $\mathcal B(\mathcal H)$. This negatively answers another of their problems.


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Additional Information

Guoxing Ji
Affiliation: College of Mathematics and Information Science, Shaanxi Normal University, Xian, 710062, People’s Republic of China
Email: gxji@snnu.edu.cn

Kichi-Suke Saito
Affiliation: Department of Mathematics, Faculty of Science, Niigata University, Niigata, 950-2181, Japan
Email: saito@math.sc.niigata-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07860-3
PII: S 0002-9939(05)07860-3
Keywords: Unitary group, wandering vector, wandering vector multiplier, von Neumann algebra.
Received by editor(s): April 30, 2003
Received by editor(s) in revised form: June 10, 2004
Published electronically: May 2, 2005
Additional Notes: The first author was supported in part by the National Natural Science Foundation of China (No.10071047), the Excellent Young Teachers Program of MOE, P.R.C and China Scholarship Council. The second author was supported in part by Grants-in-Aid for Scientific Research, Japan Society for the Promotion of Science.
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society