  In infinite dimensional Banach spaces there is no complete characterization
of the L\'evy exponents of infinitely divisible probability measures. Here we
propose \emph{a calculus on L\'evy exponents} that is derived from some random
integrals. As a consequence we prove that \emph{each} selfdecomposable measure
can by factorized as another selfdecomposable measure and its background
driving measure that is s-selfdecomposable. This complements a result from the
paper of Iksanov-Jurek-Schreiber in the Annals of Probability \textbf{32},
2004.}
