Abstract:For every fixed $\varepsilon >0$, we construct a bounded linear operator on the separable Hilbert space having an orbit which intersects every cone of aperture $\varepsilon >0$, but such that every orbit avoids a certain ball of positive radius (which depends on the orbit) and a fixed centre.
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- Frédéric Bayart
- Affiliation: Laboratoire de Mathématiques, Université Blaise Pascal, Campus des Cézeaux, F-63177 Aubière Cedex, France
- MR Author ID: 683115
- Email: Frederic.Bayart@math.univ-bpclermont.fr
- Received by editor(s): June 16, 2009
- Received by editor(s) in revised form: January 20, 2010
- Published electronically: May 17, 2010
- Communicated by: Nigel J. Kalton
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Proc. Amer. Math. Soc. 138 (2010), 4037-4043
- MSC (2010): Primary 47A16, 47B37
- DOI: https://doi.org/10.1090/S0002-9939-2010-10414-8
- MathSciNet review: 2679624