Author

Osamu Hatori

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Preprint Sep 2026

Surjective Fischer--Musz\'ely maps on positive cones of JB-algebras

We prove that every surjective Fischer--Musz\'ely map between positive cones of arbitrary JB-algebras is additive and positively homogeneous, and extends uniquely to a bounded positive linear surjection. In particular, this gives a complete affirmative answer to Moln\'ar's problem for arbitrary $C^*$-algebras. The theo...

Osamu Hatori, Shiho Oi · 0 citations

Preprint Sep 2026

Order isomorphisms on positive cones of non-unital $C^*$-algebras

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 rep...

Osamu Hatori, Shiho Oi · 1 citation