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July 2016 Linear maps between C-algebras preserving extreme points and strongly linear preservers
María J. Burgos, Antonio C. Márquez-García, Antonio Morales-Campoy, Antonio M. Peralta
Banach J. Math. Anal. 10(3): 547-565 (July 2016). DOI: 10.1215/17358787-3607288

Abstract

We study new classes of linear preservers between C-algebras and between JB-triples. Let E and F be JB-triples with e(E1). We prove that every linear map T:EF strongly preserving Brown–Pedersen quasi-invertible elements is a triple homomorphism. Among the consequences, we establish that, given two unital C-algebras A and B, for each linear map T strongly preserving Brown–Pedersen quasi-invertible elements, there exists a Jordan -homomorphism S:AB satisfying T(x)=T(1)S(x) for every xA. We also study the connections between linear maps strongly preserving Brown–Pedersen quasi-invertibility and other clases of linear preservers between C-algebras like Bergmann-zero pairs preservers, Brown–Pedersen quasi-invertibility preservers, and extreme points preservers.

Citation

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María J. Burgos. Antonio C. Márquez-García. Antonio Morales-Campoy. Antonio M. Peralta. "Linear maps between C-algebras preserving extreme points and strongly linear preservers." Banach J. Math. Anal. 10 (3) 547 - 565, July 2016. https://doi.org/10.1215/17358787-3607288

Information

Received: 22 July 2015; Accepted: 11 November 2015; Published: July 2016
First available in Project Euclid: 22 July 2016

zbMATH: 06621469
MathSciNet: MR3528347
Digital Object Identifier: 10.1215/17358787-3607288

Subjects:
Primary: 47B49
Secondary: ‎15A09, 46L05, 47B48

Rights: Copyright © 2016 Tusi Mathematical Research Group

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Vol.10 • No. 3 • July 2016
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