Geodesic
Weighted homomorphisms between $\mathrm{C}^{*}$-algebras
Documenta mathematica, Tome 30 (2025) no. 3, pp. 587-610

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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.
DOI : 10.4171/dm/1008
Classification : 47B65, 47B49
Mots-clés : C∗-algebras, weighted homomorphisms, zero-products, range-orthogonality, domain-orthogonality 
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Eusebio Gardella; Hannes Thiel. Weighted homomorphisms between $\mathrm{C}^{*}$-algebras. Documenta mathematica, Tome 30 (2025) no. 3, pp. 587-610. doi: 10.4171/dm/1008

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