Opérateurs linéaires gaussiens

We extend operators from the Cameron-Martin space to Gaussian Lusinian locally convex space. We then are allowed to give sense to the Mehler formula for every such bounded operator. An application is made to Hilbert-Schmidt operators. Next we show that capacities asociated to second quantizations of operators are tight on compact sets, and this is a general result even if the underlying space is not a Banach space.

Le deuxième auteur a exposé ce travail au colloque d'Amersfoort, août 1991.