Densely hereditarily hypercyclic sequences and large hypercyclic manifolds

We prove in this paper that if ( T n ) (Tₙ) is a hereditarily hypercyclic sequence of continuous linear mappings between two topological vector spaces X X and Y Y , where Y Y is metrizable, then there is an infinite-dimensional linear submanifold M M of X X such that each non-zero vector of M M is hypercyclic for ( T n ) (Tₙ) . If, in addition, X X is metrizable and separable and ( T n ) (Tₙ) is densely hereditarily hypercyclic, then M M can be chosen dense.