A new class of frequently hypercyclic operators

Details A new class of frequently hypercyclic operators A new class of frequently hypercyclic operators

2010-01-12

arxiv.org/abs/1001.2026v3

Mathematics

Functional Analysis

22 pages. To appear in Indiana Univ. Math. J

Scientific paper

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.

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