Lipschitzness of *-homomorphisms between C*-metric algebras  

作　　者：WU Wei 

机构地区：[1]Department of Mathematics, East China Normal University, Shanghai 200241, China

出　　处：《Science China Mathematics》2011年第11期2473-2485,共13页中国科学：数学（英文版）

基　　金：supported by the Shanghai Leading Academic Discipline Project (Project No. B407);National Natural Science Foundation of China (Grant No. 10671068)

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.

关 键 词：C^＊-metric algebra unital ^＊-homomorphism lower semicontinuous seminorm Leibniz seminorm reduced free product Lipschitz map 

分 类 号：O159[理学—数学] TM131[理学—基础数学]