Banach Journal of Mathematical Analysis

Linear maps between C-algebras preserving extreme points and strongly linear preservers

María J. Burgos, Antonio C. Márquez-García, Antonio Morales-Campoy, and Antonio M. Peralta

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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.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 3 (2016), 547-565.

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1469199409

Digital Object Identifier
doi:10.1215/17358787-3607288

Mathematical Reviews number (MathSciNet)
MR3528347

Zentralblatt MATH identifier
06621469

Subjects
Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Secondary: 15A09: Matrix inversion, generalized inverses 46L05: General theory of $C^*$-algebras 47B48: Operators on Banach algebras

Keywords
$\mathrm{C}^{*}$-algebra $\mathrm{JB}^{*}$-triple triple homomorphism linear preservers extreme points preserver strongly Brown–Pedersen quasi-invertibility preserver

Citation

Burgos, María J.; Márquez-García, Antonio C.; Morales-Campoy, Antonio; Peralta, Antonio M. Linear maps between $\mathrm{C}^{*}$ -algebras preserving extreme points and strongly linear preservers. Banach J. Math. Anal. 10 (2016), no. 3, 547--565. doi:10.1215/17358787-3607288. https://projecteuclid.org/euclid.bjma/1469199409


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