Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 47A65, 47B37, 47B99

Retrieve articles in all journals with MSC (1991): 47A65, 47B37, 47B99


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04657-2
PII: S 0002-9939(99)04657-2
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