Inductive limits of compact quantum metric spaces

2025/03/24 by Long, Botao, Sadeghi, Ghadir · 1 citation
#46L85(Primary) 46L87 #58B34(Secondary) #FOS: Mathematics #Operator Algebras (math.OA)

paper · doi:10.48550/arxiv.2503.18266

Abstract

A compact quantum metric space is a unital C^*-algebra equipped with a Lip-norm. Let \(A_n, L_n)\ be a sequence of compact quantum metric spaces, and let ϕ_n:A_n→ A_n+1 be a unital ^*-homomorphism preserving Lipschitz elements for n≥ 1. We show that there exists a compact quantum metric space structure on the inductive limit \varinjlim(A_n,ϕ_n) by means of the inverse limit of the state spaces \S(A_n)\. We also give some sufficient conditions that two inductive limits of compact quantum metric spaces are Lipschitz isomorphic.

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• Tracially lyriform C^*-algebras

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