Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras

We study holomorphic maps between C*-algebras A and B, when f:BA(0,ϱ)→B is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball U=BA(0,δ). If we assume that f is orthogonality preserving and orthogonally additive on Asa∩U and f(U) contains an invertible element in B, then there exist a sequence (hn) in B** and Jordan *-homomorphisms Θ,Θ~:M(A)→B** such that f(x)=∑n=1∞hnΘ~(an)=∑n=1∞Θ(an)hn uniformly in a∈U. When B is abelian, the hypothesis of B being unital and f(U)∩inv(B)≠∅ can be relaxed to get the same statement