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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| 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. |
| format | Article |
| id | doaj-art-f4ac3013582e409b96981dd5b2bd049c |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| 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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