Year: 2026
Type: preprint
Abstract: Let $A$ and $B$ be $C^*$-algebras, not necessarily unital, and let $T:A_+\to B_+$ be a positively homogeneous order isomorphism. We first prove that $T$ is additive and extends uniquely to a bounded real-linear order isomorphism between the self-adjoint parts of $A$ and $B$. Passing to the biduals, we then obtain a representation theorem for positively homogeneous order isomorphisms. Finally, we study surjective maps between the positive cones of $C^*$-algebras, again not necessarily unital, which preserve the norm of the arithmetic mean. This extends a previous result by removing the assumption that at least one of the algebras is unital.
Source: arXiv (Cornell University)
Authors: Hatori, Osamu, Oi, Shiho
Institution: Niigata University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213914562