Additive Hermitian idempotent preservers between operator algebras (Q2235957)

Let \(M_{n}\) be the set of \(n\times n\) matrices and let \(H_n\) be the subset of hermitian matrices. In the first half of the paper the authors give a detailed description of the additive maps \(L \colon H_n \to H_m\) that preserve hermitian idempotents. In particular, they show that the behave like a Jordan \(*\)-homomorphism on \(\operatorname{span}_{\mathbb{Q}} P(M_n)\). In the second half, they extend this result to von Neumann algebras in the spirit of the Bunce-Wright-Dye theorem.