  We study a hypercyclicity property of linear dynamical systems: a bounded
linear operator T acting on a separable infinite-dimensional Banach space X is
said to be hypercyclic if there exists a vector x in X such that {T^{n}x : n>0}
is dense in X, and frequently hypercyclic if there exists x in X such that for
any non empty open subset U of X, the set {n>0 ; T^n x \in U} has positive
lower density. We prove that if T is a bounded operator on X which has
"sufficiently many" eigenvectors associated to eigenvalues of modulus 1 in the
sense that these eigenvectors are perfectly spanning, then T is automatically
frequently hypercyclic.
