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

الأصل · EN

We study holomorphic maps between C*-algebras A and B. When f:Bₐ (0,) 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, Θ: M(A) → B** such that f(x) = ∑ₙ₌₁∞ hₙ Θ (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.