Orthogonally additive holomorphic functions on C^*-algebras

@article{Peralta2012OrthogonallyAH,
  title={Orthogonally additive holomorphic functions on C^*-algebras},
  author={Antonio M. Peralta and Daniele Puglisi},
  journal={Operators and Matrices},
  year={2012},
  pages={621-629}
}
Let A be a C ∗ -algebra. We prove that a holomorphic function of bounded type f : A → C is orthogonally additive on Asa if, and only if, it is additive on elements having zeroproduct if, and only if, there exist a positive functional φ in A∗ , a sequence (ψn) in L1(A∗∗,φ) and a power series holomorphic function h in Hb(A,A∗) such that h(a) = ∞ ∑ k=1 ψk ·ak and f (a) = 〈1A∗∗ ,h(a)〉 = ∫ h(a) dφ , for every a in A , where 1 A∗∗ denotes the unit element in A ∗∗ and L1(A∗∗,φ) is a noncommutative L1… 
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