# Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras

@article{Garces2013OrthogonallyAA, title={Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras}, author={Jorge J. Garc'es and Antonio M. Peralta and Daniele Puglisi and Mar'ia Isabel Ram'irez}, journal={Abstract and Applied Analysis}, year={2013}, volume={2013}, pages={1-9} }

We study holomorphic maps between C-algebras and , when is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball . If we assume that is orthogonality preserving and orthogonally additive on and contains an invertible element in , then there exist a sequence in and Jordan -homomorphisms such that uniformly in . When is abelian, the hypothesis of being unital and can be relaxed to get the same statement.

## 11 Citations

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Let $A,B$ be C*-algebras, $B_A(0;r)$ the open ball in $A$ centered at $0$ with radius $r>0$, and $H:B_A(0;r)\to B$ an orthogonally additive holomorphic map. If $H$ is zero product preserving on…

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Orthogonally additive and orthogonally multiplicative holomorphic functions of matrices

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Let $H:M_m\to M_m$ be a holomorphic function of the algebra $M_m$ of complex $m\times m$ matrices. Suppose that $H$ is orthogonally additive and orthogonally multiplicative on self-adjoint elements.…

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