2013/10/01 by Garcés, Jorge J., Peralta, Antonio M., Puglisi, Daniele +1
#FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)
paper · doi:10.48550/arxiv.1310.0407
We study holomorphic maps between C^*-algebras A and B. When f:BA (0,\varrho) \longrightarrow B is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball U=BA(0,δ) and we assume that f is orthogonality preserving on Asa∩ U, orthogonally additive on U and f(U) contains an invertible element in B, then there exist a sequence (hn) in B** and Jordan ^*-homomorphisms Θ, \widetildeΘ : M(A) → B** such that f(x) = ∑n=1^∞ hn \widetildeΘ (an)= ∑n=1^∞ Θ (an) hn, uniformly in a∈ U. When B is abelian the hypothesis of B being unital and f(U)∩ \hboxinv (B) ≠ ∅ can be relaxed to get the same statement.