Abstract
We develop an intrinsic C*-algebraic model of a Gaussian field over a Hilbert space H. The model contains Gross’ abstract Wiener spaces, Malliavin's Gaussian probability spaces and Itô's Wiener space. Within this model we exhibit correspondences between algebraic properties of symmetric Fock space over H and analytic properties of Malliavin calculus. As a consequence we obtain, prima facie, a canonical setting for Malliavin calculus.
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