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

Menet, Quentin

doi:10.1090/S0002-9939-2015-12444-6

Existence and non-existence of frequently hypercyclic subspaces for weighted shifts
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Proc. Amer. Math. Soc. 143 (2015), 2469-2477 Request permission

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)].

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