Abstract
We construct a Banach space operator \({T \in B(X)}\) such that the set J T (0) has a nonempty interior but J T (0) ≠ X. This gives a negative answer to a problem raised by Costakis and Manoussos (J. Oper. Theory [in press], 2011).
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References
Bourdon P.S., Feldman N.S.: Somewhere dense orbits are everywhere dense. Indiana Univ. Math. J. 52, 811–819 (2003)
Costakis, G., Manoussos, A.: J-class operators and hypercyclicity. J. Oper. Theory (to appear) (2011)
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The research was supported by grants 201/09/0473 of GA ČR, IAA100190903 of GA AV and Institution Research Plan AV OZ 10190503.
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Azimi, M.R., Müller, V. A note on J-sets of linear operators. RACSAM 105, 449–453 (2011). https://doi.org/10.1007/s13398-011-0042-6
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DOI: https://doi.org/10.1007/s13398-011-0042-6