Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
Garcés Pérez, Jorge José
Peralta, Antonio Miguel
Puglisi, Daniele
Ramírez, María Isabel
Polynomials
Spaces
C(K)
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.
2014-04-23T09:42:52Z
2014-04-23T09:42:52Z
2013
info:eu-repo/semantics/article
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]
http://hdl.handle.net/10481/31360
10.1155/2013/415354
eng
http://creativecommons.org/licenses/by-nc-nd/3.0/
info:eu-repo/semantics/openAccess
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