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

 

On the existence of $ J$-class operators on Banach spaces


Author: Amir Bahman Nasseri
Journal: Proc. Amer. Math. Soc. 140 (2012), 3549-3555
MSC (2000): Primary 47A16; Secondary 37B99, 54H20
Published electronically: February 24, 2012
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Abstract: In this paper we answer in the negative the question raised by G. Costakis and A. Manoussos whether there exists a $ J$-class operator on every non-separable Banach space. In particular we show that there exists a non-separable Banach space constructed by S. Argyros, A. Arvanitakis and A. Tolias such that the $ J$-set of every operator on this space has empty interior for each non-zero vector. On the other hand, on non-separable spaces which are reflexive there always exists a $ J$-class operator.


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Additional Information

Amir Bahman Nasseri
Affiliation: Fakultät für Mathematik, Technische Universität Dortmund, D-44221 Dortmund, Germany
Email: amirbahman@hotmail.de

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11200-6
PII: S 0002-9939(2012)11200-6
Keywords: $J$-class operators, hypercyclicity
Received by editor(s): September 28, 2010
Received by editor(s) in revised form: April 13, 2011, and April 15, 2011
Published electronically: February 24, 2012
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.