摘要
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.
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.
基金
supported by the Shanghai Leading Academic Discipline Project (Project No. B407)
National Natural Science Foundation of China (Grant No. 10671068)
关键词
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莱布尼茨
C^＊-metric algebra, unital ^＊-homomorphism, lower semicontinuous seminorm, Leibniz seminorm reduced free product, Lipschitz map
