We provide criteria for the existence of upper frequently hypercyclic
subspaces and for common hypercyclic subspaces, which include the following
consequences. There exist frequently hypercyclic operators with
upper-frequently hypercyclic subspaces and no frequently hypercyclic subspace.
On the space of entire functions, each differentiation operator induced by a
non-constant polynomial supports an upper frequently hypercyclic subspace, and
the family of its non-zero scalar multiples has a common hypercyclic subspace.
A question of Costakis and Sambarino on the existence of a common hypercyclic
subspace for a certain uncountable family of weighted shift operators is also
answered.Comment: 30 page
