Frédéric Bayart, 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.
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