Lipschitzness of *-homomorphisms between C*-metric algebras

2009/01/18 by Wei Wu, Wu, Wei
Mathematics · Physics and Astronomy · #46L05 #46L87 #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Noncommutative and Quantum Gravity Theories #Operator Algebras (math.OA) #math.OA #msc:46L05 #msc:46L87

paper · pdf · doi:10.48550/arxiv.0901.2695

10 pages. *-homomorphism between C*-metric algebras added to Definition 2.5. An error in Proposition 3.2 is corrected. A few minor improvements elsewhere

openalex publication_date 2009/01/18 · arxiv created 2009/01/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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. It results that the free product of two Lipschitz unital *-homomorphisms between C*-metric algebras coming from *-filtrations is still a Lipschitz unital *-homomorphism.

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