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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 power series of backward shift operators


Author: Félix Martínez-Giménez
Journal: Proc. Amer. Math. Soc. 135 (2007), 1741-1752
MSC (2000): Primary 47A16, 47B37, 37D45, 46A04, 46A45
Published electronically: January 31, 2007
MathSciNet review: 2286084
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Abstract: We study when the operator $ f(B_w)$ is chaotic in the sense of Devaney on a Köthe echelon sequence space, where $ B_w$ is a weighted backward shift and $ f(z)=\sum_{j=0}^\infty f_j z^j$ is a formal power series.


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Additional Information

Félix Martínez-Giménez
Affiliation: Departamento de Matemática Aplicada, E.T.S.I. Agrónomos, Universidad Politécnica de Valencia, Camino Vera s/n, E-46022 Valencia, Spain
Email: fmarting@mat.upv.es

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08658-3
PII: S 0002-9939(07)08658-3
Keywords: Chaotic operators, hypercyclic operators, weighted backward shifts
Received by editor(s): March 14, 2005
Received by editor(s) in revised form: January 20, 2006
Published electronically: January 31, 2007
Additional Notes: This work was supported by FEDER and MCYT, Proyecto No. MTM2004–02262 and AVCIT Grupo 03/050
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.