A new class of frequently hypercyclic operators

الأصل · EN

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 Tⁿx: 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; Tⁿ x ∈ 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.