Orthogonally additive, orthogonality preserving, holomorphic mappings between C*-algebras

We study holomorphic maps between C${}^{\ast }$-algebras $A$ and $B$. When $f:B_A (0,\varrho) \longrightarrow B$ is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball $U=B_A(0,\delta )$ and we assume that $f$ is orthogonality preserving on $A_{sa}\cap U$, orthogonally additive on $U$ and $f(U)$ contains an invertible element in $B$, then there exist a sequence $(h_n)$ in $B^{\ast \ast }$ and Jordan ${}^{\ast }$-homomorphisms $\Theta, \widetilde{\Theta} : M(A) \to B^{**}$suchthat$$ f(x) = \sum_{n=1}^\infty h_n \widetilde{\Theta} (a^n)= \sum_{n=1}^\infty {\Theta} (a^n) h_n,$$uniformlyin$a\in U$\mathrm{.}When$B$isabelianthehypothesisof$B$beingunitaland$f(U)\cap \hbox{inv} (B) \neq \emptyset$ can be relaxed to get the same statement.