We study new classes of linear preservers between -algebras and between -triples. Let and be -triples with . We prove that every linear map strongly preserving Brown–Pedersen quasi-invertible elements is a triple homomorphism. Among the consequences, we establish that, given two unital -algebras and , for each linear map strongly preserving Brown–Pedersen quasi-invertible elements, there exists a Jordan -homomorphism satisfying for every . We also study the connections between linear maps strongly preserving Brown–Pedersen quasi-invertibility and other clases of linear preservers between -algebras like Bergmann-zero pairs preservers, Brown–Pedersen quasi-invertibility preservers, and extreme points preservers.
"Linear maps between -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