A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra t...A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra to another one is necessarily Lipschitz. We come to the result that the free product of two unital completely Lipschitz contractive *-homomorphisms from upper related C*-metric algebras coming from *-filtrations to those which are lower related is a unital Lipschitz *-homomorphism.展开更多
基金supported by the Shanghai Leading Academic Discipline Project (Project No. B407)National Natural Science Foundation of China (Grant No. 10671068)
文摘A C*-metric algebra consists of a unital C*-algebra and a Leibniz Lip-norm on the C*-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital *-homomorphism from a C*-metric algebra to another one is necessarily Lipschitz. We come to the result that the free product of two unital completely Lipschitz contractive *-homomorphisms from upper related C*-metric algebras coming from *-filtrations to those which are lower related is a unital Lipschitz *-homomorphism.
