On the existence of 𝐽-class operators on Banach spaces

Nasseri, Amir

doi:10.1090/S0002-9939-2012-11200-6

On the existence of $J$-class operators on Banach spaces
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by Amir Bahman Nasseri PDF

Proc. Amer. Math. Soc. 140 (2012), 3549-3555 Request permission

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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