We study new classes of linear preservers between C$^*$-algebras andJB$^*$-triples. Let $E$ and $F$ be JB$^*$-triples with $\partial_{e} (E_1)$. Weprove that every linear map $T:E\to F$ strongly preserving Brown-Pedersenquasi-invertible elements is a triple homomorphism. Among the consequences, weestablish that, given two unital C$^*$-algebras $A$ and $B,$ for each linearmap $T$ strongly preserving Brown-Pedersen quasi-invertible elements, thenthere exists a Jordan $^*$-homomorphism $S: A\to B$ satisfying $T(x) = T(1)S(x)$, for every $x\in A$. We also study the connections between linear mapsstrongly preserving Brown-Pedersen quasi-invertibility and other clases oflinear preservers between C$^*$-algebras like Bergmann-zero pairs preservers,Brown-Pedersen quasi-invertibility preservers and extreme points preservers.
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机译：我们研究了C $ ^ * $-代数和JB $ ^ * $-三元组之间的新型线性保留子。假设$ E $和$ F $为带有$ \ partial_ {e}（E_1）$的JB $ ^ * $三元组。我们证明，每个强烈保留Brown-Pedersenquasi可逆元素的线性映射$ T：E \ F $是三重同态。在结果中，我们确定，给定两个单位C $ ^ * $-代数$ A $和$ B，对于每个线性映射$ T $，它们都保留了Brown-Pedersen拟可逆元素，则存在约旦$ ^ * $-同态$ S：A \ to B $满足$ T（x）= T（1）S（x）$，对于A $中的每个$ x \。我们还研究了严格保留Brown-Pedersen拟可逆性的线性映射与C $ ^ * $代数之间的线性保留剂的其他类之间的联系，例如Bergmann零对保存器，Brown-Pedersen拟可逆性保存器和极点保存器。
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