2010/01/12 by Grivaux, Sophie
#37A05 #46B09 #46B15 #47A16 #47A35 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1001.2026
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.