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: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |