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

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 Asa∩U and f(U) contains an invertible el...

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Main Authors: Jorge J. Garcés, Antonio M. Peralta, Daniele Puglisi, María Isabel Ramírez
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/415354
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author Jorge J. Garcés
Antonio M. Peralta
Daniele Puglisi
María Isabel Ramírez
author_facet Jorge J. Garcés
Antonio M. Peralta
Daniele Puglisi
María Isabel Ramírez
author_sort Jorge J. Garcés
collection DOAJ
description 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 Asa∩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∞hnΘ~(an)=∑n=1∞Θ(an)hn uniformly in a∈U. When B is abelian, the hypothesis of B being unital and f(U)∩inv(B)≠∅ can be relaxed to get the same statement.
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institution Kabale University
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series Abstract and Applied Analysis
spelling doaj-art-f4ac3013582e409b96981dd5b2bd049c2025-02-03T01:01:48ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/415354415354Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-AlgebrasJorge J. Garcés0Antonio M. Peralta1Daniele Puglisi2María Isabel Ramírez3Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, SpainDepartamento de Análisis Matemático, Facultad de Ciencias, Universidad de Granada, 18071 Granada, SpainDipartimento di Matematica e Informatica, Università di Catania, 95125 Catania, ItalyDepartamento de Algebra y Análisis Matemático, Universidad de Almería, 04120 Almería, SpainWe 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 Asa∩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∞hnΘ~(an)=∑n=1∞Θ(an)hn uniformly in a∈U. When B is abelian, the hypothesis of B being unital and f(U)∩inv(B)≠∅ can be relaxed to get the same statement.http://dx.doi.org/10.1155/2013/415354
spellingShingle Jorge J. Garcés
Antonio M. Peralta
Daniele Puglisi
María Isabel Ramírez
Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
Abstract and Applied Analysis
title Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
title_full Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
title_fullStr Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
title_full_unstemmed Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
title_short Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
title_sort orthogonally additive and orthogonality preserving holomorphic mappings between c algebras
url http://dx.doi.org/10.1155/2013/415354
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