The author shows that for every open subset
of a Banach space there exists a unique Banach space
and a holomorphic mapping
such that every Banach valued bounded holomorphic function on
can be written as a composition of
and a Banach valued continuous linear mapping on
. This gives a linearization of bounded holomorphic mappings and shows that
has the structure of a dual Banach space. Applications to the study of holomorphic mappings of compact type, the approximation property and polynomials are given using this linearization result.