Maps preserving the diamond partial order
The present paper is devoted to the study of the diamond partial order in general C*-algebras and the description of linearmaps preserving this partial order
math.OA↗
arXiv subjects
Antonio Morales-Campoy
Publications and source records attributed to Antonio Morales-Campoy.
Minus partial order and linear preservers
In this paper we investigate the properties of minus partial order in unital rings. We generalize several results well known for matrices and bounded linear operators on Banach spaces. We also study linear maps preserving the minus partial order in unital semisimple Banach algebras with essential socle.
math.FA↗
Linear maps between C*-algebras preserving extreme points and strongly linear preservers
We study new classes of linear preservers between C$^*$-algebras and JB$^*$-triples. Let $E$ and $F$ be JB$^*$-triples with $\partial_{e} (E_1)$. We prove that every linear map $T:E\to F$ 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, then there 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 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.
math.OA↗