Ergodic and dynamical properties of m-isometries

An example of a weakly ergodic 3-isometry is provided in [3], we give new examples of weakly ergodic 3-isometries and study numerically hypercyclic m-isometries on finite and infinite dimensional Hilbert spaces. In particular, all weakly ergodic strict 3-isometries on a Hilbert space are weakly numerically hypercyclic. Adjoints of unilateral forward weighted shifts which are strict m-isometries on ℓ2(N) are shown to be hypercyclic.