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Proceedings of the American Mathematical Society

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On hypercyclic operators on Banach spaces

Author: Luis Bernal-González
Journal: Proc. Amer. Math. Soc. 127 (1999), 1003-1010
MSC (1991): Primary 47A65; Secondary 47B37, 47B99
MathSciNet review: 1476119
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Abstract: We provide in this paper a direct and constructive proof of the following fact: for a Banach space $X$ there are bounded linear operators having hypercyclic vectors if and only if $X$ is separable and dim$\, X = \infty $. This is a special case of a recent result, which in turn solves a problem proposed by S. Rolewicz.

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Luis Bernal-González
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain

Keywords: Hypercyclic vector, linear operator, infinite-dimensio\-nal separable Banach space, biorthogonal system, backward weighted shift
Received by editor(s): May 29, 1997
Received by editor(s) in revised form: July 6, 1997
Additional Notes: The author’s research was supported in part by DGES grant #PB93–0926 and the Junta de Andalucıá.
Communicated by: David R. Larson
Article copyright: © Copyright 1999 American Mathematical Society