Existence and non-existence of frequently hypercyclic subspaces for weighted shifts
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Abstract:
We study the existence and the non-existence of frequently hypercyclic subspaces of frequently hypercyclic operators living on Banach spaces. In particular, we give an example of a weighted shift on $l^p$ possessing a frequently hypercyclic subspace and an example of a frequently hypercyclic weighted shift on $l^p$ possessing a hypercyclic subspace but no frequently hypercyclic subspace. The latter example allows us to answer positively Problem 1 posed by Bonilla and Grosse-Erdmann in [Monatsh. Math. 168 (2012)].References
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Additional Information
- Quentin Menet
- Affiliation: Institut de Mathématique, Université de Mons, 20 Place du Parc, 7000 Mons, Belgique
- MR Author ID: 962506
- ORCID: 0000-0002-9334-1837
- Email: Quentin.Menet@umons.ac.be
- Received by editor(s): September 30, 2013
- Received by editor(s) in revised form: January 7, 2014
- Published electronically: January 16, 2015
- Additional Notes: The author was supported by a grant of FRIA
- Communicated by: Pamela B. Gorkin
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 143 (2015), 2469-2477
- MSC (2010): Primary 47A16
- DOI: https://doi.org/10.1090/S0002-9939-2015-12444-6
- MathSciNet review: 3326029