This is an announcement for the paper "On the existence of J-class operators" by Amir Nasseri.

Abstract: In this note 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 par- ticular we show that there exists a non-separable Banach space constructed by A.Arvanitakis, S.Argyros 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 exist a J-class operator.

Archive classification: math.FA

Remarks: 8 pages, hypercyclicity, J-class operators

Submitted from: amir.nasseri@uni-dortmund.de

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1009.3461

or

http://arXiv.org/abs/1009.3461