Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
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Hindawi Publishing Corporation
Garcés, J.J.; Peralta, A.M.; Puglisi, D.; Ramírez, M.I. Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras. Abstract and Applied Analysis, 2013: 415354 (2013). [http://hdl.handle.net/10481/31360]
SponsorshipThe authors are partially supported by the Spanish Ministry of Economy and Competitiveness, D.G.I. Project no. MTM2011-23843, and Junta de Andalucía Grant FQM3737.
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 A s a ∩ 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 ∞ h n Θ (an) = ∑n = 1 ∞ Θ (an) hn uniformly in a ∈ U. When B is abelian, the hypothesis of B being unital and f (U) ∩ i n v (B) ≠ ∅ can be relaxed to get the same statement.