Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 
 

 

Existence and non-existence of frequently hypercyclic subspaces for weighted shifts


Author: Quentin Menet
Journal: Proc. Amer. Math. Soc. 143 (2015), 2469-2477
MSC (2010): Primary 47A16
DOI: https://doi.org/10.1090/S0002-9939-2015-12444-6
Published electronically: January 16, 2015
MathSciNet review: 3326029
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 47A16

Retrieve articles in all journals with MSC (2010): 47A16


Additional Information

Quentin Menet
Affiliation: Institut de Mathématique, Université de Mons, 20 Place du Parc, 7000 Mons, Belgique
Email: Quentin.Menet@umons.ac.be

DOI: https://doi.org/10.1090/S0002-9939-2015-12444-6
Keywords: Hypercyclicity, frequent hypercyclicity, hypercyclic subspaces, weighted shifts
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
Article copyright: © Copyright 2015 American Mathematical Society