On the existence of $J$-class operators on Banach spaces
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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.References
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Additional Information
- Amir Bahman Nasseri
- Affiliation: Fakultät für Mathematik, Technische Universität Dortmund, D-44221 Dortmund, Germany
- Email: amirbahman@hotmail.de
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 3549-3555
- MSC (2000): Primary 47A16; Secondary 37B99, 54H20
- DOI: https://doi.org/10.1090/S0002-9939-2012-11200-6
- MathSciNet review: 2929023