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

Jorge J. Garcés, Antonio M. Peralta, Daniele Puglisi and María Isabel Ramírez

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: 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.

Date: 2013
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2013/415354

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:415354

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().