Abstract and Applied Analysis

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

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

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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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 415354, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449674

Digital Object Identifier
doi:10.1155/2013/415354

Mathematical Reviews number (MathSciNet)
MR3147830

Zentralblatt MATH identifier
1292.32001

Citation

Garcés, Jorge J.; Peralta, Antonio M.; Puglisi, Daniele; Ramírez, María Isabel. Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 415354, 9 pages. doi:10.1155/2013/415354. https://projecteuclid.org/euclid.aaa/1393449674


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