Frédéric Bayart and Sophie Grivaux

We give conditions for an operator $T$ on a complex separable Banach space $X$ with sufficiently many eigenvectors associated to eigenvalues of modulus $1$ to admit a non-degenerate invariant Gaussian measure with respect to which it is weak-mixing. The existence of such a measure depends on the geometry of the Banach space and on the possibility of parametrizing the $\mathbb{T}$-eigenvector fields of $T$ in a regular way. We also investigate the connection with frequent hypercyclicity.

2000 Mathematics Subject Classification: 47A16, 47A35, 46B09, 46B25, 37A05, 37A25, 60G15.

E-mail:
Frederic.Bayart@math.u-bordeaux1.fr
grivaux@math.univ-lille1.fr