TAYLOR MAP ON GROUPS ASSOCIATED WITH A II1-FACTOR

Abstract

A notion of the heat kernel measure is introduced for the L2 completion of a hyperfinite II1-factor with respect to the trace. Some properties of this measure are derived from the corresponding stochastic differential equation. Then the Taylor map is studied for a space of holomorphic functions square integrable with respect to the heat kernel measure. We also define a skeleton map from this space to a Hilbert space of holomorphic functions on a certain Cameron–Martin group. This group is a subgroup of the group of invertible elements of the II1-factor.