Quantum metrics on the tensor product of a commutative C*-algebra and an AF C*-algebra

2019/07/17 by Konrad Aguilar, Aguilar, Konrad
Mathematics · #46L30 #46L89 #58B34 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.1907.07357

openalex publication_date 2019/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a compact metric space X and a unital AF algebra A equipped with a faithful tracial state, we place quantum metrics on the tensor product of C(X) and A given established quantum metrics on C(X) and A from work with Bice and Latrémolière. We prove the inductive limit of C(X) tensor A given by A is a metric limit in the Gromov-Hausdorff propinquity. We show that our quantum metric is compatible with the tensor product by producing a Leibniz rule on elementary tensors and showing the diameter of our quantum metric on the tensor product is bounded above the diameter of the Cartesian product of the quantum metric spaces. We provide continuous families of C(X) tensor A which extends our previous results with Latrémolière on UHF algebras.

Citations

• Descriptive set theory and forcing; How to prove theorems about Borel sets the hard way
• Convergence of Quotients of AF Algebras in Quantum Propinquity by Convergence of Ideals

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• Quantum metrics on noncommutative spaces
• Standard homogeneous C*-algebras as compact quantum metric spaces
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