Invariant Gaussian measures for operators on Banach spaces and linear dynamics

• Autores: Frédéric Bayart, Sophie Grivaux
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 94, Nº 1, 2007, págs. 181-210
• Idioma: inglés
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• Resumen

  • 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.