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Suppose $\lambda_1$ and $\lambda_2$ are infinitely divisible Radon measureson real Banach spaces $E_1$ and $E_2$, respectively and let $T:E_{1}\rightarrow E_{2}$ be a Borel measurable mapping so that $T(\lambda_1) * \rho =\lambda_2 $ for some Radon probability measure $\rho$ on $E_{2}$. Extendingprevious results for the Gaussian and the Poissonian case, we study the problemof representing the `transition operator' $P_{T}:L^{p}(E_{2}, \lambda_{2})\rightarrow L^{p}(E_{1}, \lambda_{1})$ given by $$ P_{T}f(x) =\int_{E_{2}}f(T(x) + y)d\rho(y) %% d\rho(y) instead of \rho(dy) in order tounify notations $$ as the second quantisation of a contraction operator actingbetween suitably chosen `reproducing kernel Hilbert spaces' associated with$\lambda_1$ and $\lambda_2$.

Second quantisation for skew convolution products of infinitely divisible measures