Proceedings of the American Mathematical Society

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



On commutativity of the commutant of strongly irreducible operator

Author: Jue-Xian Li
Journal: Proc. Amer. Math. Soc. 140 (2012), 167-171
MSC (2010): Primary 47B37; Secondary 47C05
Published electronically: May 18, 2011
MathSciNet review: 2833529
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Abstract: In 2006, C. L. Jiang and Z. Y. Wang posed an open problem: If $ T$ is a strongly irreducible operator, is $ {\mathcal{A}}'(T)/{\rm rad} {\mathcal A}'(T)$ commutative? They conjectured that the answer is positive. In this paper, to negatively answer their problem, a counterexample is given.

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Jue-Xian Li
Affiliation: School of Mathematics, Liaoning University, 110036, Shenyang, People’s Republic of China

Keywords: Strongly irreducible operator, operator weighted shifts.
Received by editor(s): October 28, 2010
Published electronically: May 18, 2011
Additional Notes: This project is supported by the National Natural Science Foundation of China (No. 10971079).
Communicated by: Richard Rochberg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.