  We study measures in Banach space which arise as the skew convolution product
of two other measures where the convolution is deformed by a skew map. This is
the structure that underlies both the theory of Mehler semigroups and operator
self-decomposable measures. We show how that given such a set-up the skew map
can be lifted to an operator that acts at the level of function spaces and
demonstrate that this is an example of the well known functorial procedure of
second quantisation. We give particular emphasis to the case where the product
measure is infinitely divisible and study the second quantisation process in
some detail using chaos expansions when this is either Gaussian or is generated
by a Poisson random measure.
