Weighted homomorphisms between C*-algebras

Journal article, 2025

We show that a bounded, linear map between C^*-algebras is a weighted *-homomorphism (the central compression of a *-homomorphism) if and only if it preserves zero-products, range-orthogonality, and domain-orthogonality. It follows that a self-adjoint, bounded, linear map is a weighted *-homomorphism if and only if it preserves zero-products. As an application we show that a linear map between C^*-algebras is completely positive, order zero in the sense of Winter– Zacharias if and only if it is positive and preserves zero-products.