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Abstract and Applied Analysis
Volume 2013, Article ID 415354, 9 pages
http://dx.doi.org/10.1155/2013/415354
Research Article

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

1Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, Spain
2Dipartimento di Matematica e Informatica, Università di Catania, 95125 Catania, Italy
3Departamento de Algebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain

Received 1 October 2013; Accepted 27 November 2013

Academic Editor: Ngai-Ching Wong

Copyright © 2013 Jorge J. Garcés et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.