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2013 Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras
Jorge J. Garcés, Antonio M. Peralta, Daniele Puglisi, María Isabel Ramírez
Abstr. Appl. Anal. 2013(SI45): 1-9 (2013). DOI: 10.1155/2013/415354

Abstract

We study holomorphic maps between C * -algebras A and B , when f : B A ( 0 , ϱ ) B is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball U = B A ( 0 , δ ) . If we assume that f is orthogonality preserving and orthogonally additive on A s a U and f ( U ) contains an invertible element in B , then there exist a sequence ( h n ) in B * * and Jordan * -homomorphisms Θ , Θ ~ : M ( A ) B * * such that f ( x ) = n = 1 h n Θ ~ ( a n ) = n = 1 Θ ( a n ) h n uniformly in a U . When B is abelian, the hypothesis of B being unital and f ( U ) i n v ( B ) can be relaxed to get the same statement.

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Jorge J. Garcés. Antonio M. Peralta. Daniele Puglisi. María Isabel Ramírez. "Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras." Abstr. Appl. Anal. 2013 (SI45) 1 - 9, 2013. https://doi.org/10.1155/2013/415354

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1292.32001
MathSciNet: MR3147830
Digital Object Identifier: 10.1155/2013/415354

Rights: Copyright © 2013 Hindawi

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