Densely hereditarily hypercyclic sequences and large hypercyclic manifolds

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