Strong mixing measures for linear operators and frequent hypercyclicity

Abstract

We construct strongly mixing invariant measures with full support for operators on F-spaces which satisfy the Frequent Hypercyclicity Criterion. For unilateral backward shifts on sequence spaces, a slight modification shows that one can even obtain exact invariant measures.

7 pages. arXiv admin note: substantial text overlap with arXiv:1206.1978

Cited by in corpus (7)

• Linear dynamical systems on Hilbert spaces: typical properties and explicit examples
• Linear Dynamical Systems
• Strong mixing measures for $C_0$-semigroups
• Chaotic behaviour on invariant sets of linear operators
• Frequently hypercyclic $C$-distribution semigroups and their generalizations
• Frequent universality criterion and densities
• Hypercyclic behavior of some non-convolution operators on $H({\mathbb{C}}^N)$