Strong mixing measures for linear operators and frequent hypercyclicity

TL;DR

This paper constructs strongly mixing invariant measures for certain linear operators, demonstrating their hypercyclicity properties and extending results to specific shift operators with exact measures.

Contribution

It introduces methods to build strongly mixing invariant measures for operators satisfying the Frequent Hypercyclicity Criterion, including exact measures for unilateral backward shifts.

Findings

Constructed strongly mixing invariant measures for operators on F-spaces.

Extended results to unilateral backward shifts with exact invariant measures.

Demonstrated the applicability of the Frequent Hypercyclicity Criterion to measure construction.

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.