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

 

Chaos for Cowen-Douglas operators


Authors: Bingzhe Hou, Puyu Cui and Yang Cao
Journal: Proc. Amer. Math. Soc. 138 (2010), 929-936
MSC (2000): Primary 47B37, 47B99; Secondary 54H20, 37B99
Published electronically: October 28, 2009
MathSciNet review: 2566559
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Abstract: In this article, we provide a sufficient condition which gives Devaney chaos and distributional chaos for Cowen-Douglas operators. In fact, we obtain a distributionally chaotic criterion for bounded linear operators on Banach spaces.


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Additional Information

Bingzhe Hou
Affiliation: Department of Mathematics, Jilin University, 130012, Changchun, People’s Republic of China
Email: houbz@jlu.edu.cn

Puyu Cui
Affiliation: Department of Mathematics, Dalian University of Technology, 116024, Dalian, People’s Republic of China
Email: cuipuyu1234@sina.com.cn

Yang Cao
Affiliation: Department of Mathematics, Jilin University, 130012, Changchun, People’s Republic of China
Email: caoyang@jlu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10046-1
PII: S 0002-9939(09)10046-1
Keywords: Cowen-Douglas operators, strongly mixing, Devaney chaos, distributional chaos.
Received by editor(s): January 4, 2009
Received by editor(s) in revised form: April 16, 2009
Published electronically: October 28, 2009
Additional Notes: The first author is supported by the Youth Foundation of the Department of Mathematics, Jilin University
Communicated by: Bryna Kra
Article copyright: © Copyright 2009 American Mathematical Society