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.
1
University of Gothenburg and Chalmers University of Technology, Gothenburg, Sweden
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
@article{10_4171_dm_1008,
author = {Eusebio Gardella and Hannes Thiel},
title = {Weighted homomorphisms between $\mathrm{C}^{*}$-algebras},
journal = {Documenta mathematica},
pages = {587--610},
year = {2025},
volume = {30},
number = {3},
doi = {10.4171/dm/1008},
url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/1008/}
}
TY - JOUR
AU - Eusebio Gardella
AU - Hannes Thiel
TI - Weighted homomorphisms between $\mathrm{C}^{*}$-algebras
JO - Documenta mathematica
PY - 2025
SP - 587
EP - 610
VL - 30
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/dm/1008/
DO - 10.4171/dm/1008
ID - 10_4171_dm_1008
ER -
