  We study the existence and the non-existence of frequently hypercyclic
subspaces in Banach spaces. In particular, we give an example of a weighted
shift on lp possessing a frequently hypercyclic subspace and an example of a
frequently hypercyclic weighted shift on lp 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)].
