  Let (H,B) be an abstract Wiener space and let \mu_{s} be the Gaussian measure
on B with variance s. Let \Delta be the Laplacian (*not* the number operator),
that is, a sum of squares of derivatives associated to an orthonormal basis of
H. I will show that the heat operator \exp(t\Delta/2) is a contraction operator
from L^2(B,\mu_{s} to L^2(B,\mu_{s-t}), for all t<s. More generally, the heat
operator is a contraction from L^p(B,\mu_{s}) to L^q(B,\mu_{s-t}) for t<s,
provided that p and q satisfy (p-1)/(q-1) \leq s/(s-t).
  I give two proofs of this result, both very elementary.
