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Lipschitz isomorphisms of compact quantum metric spaces

Volume 261 / 2021

Botao Long, Wei Wu Studia Mathematica 261 (2021), 157-185 MSC: Primary 46L85; Secondary 46L87, 54E40, 58B34. DOI: 10.4064/sm200316-17-11 Published online: 3 June 2021


A compact quantum metric space is a complete order unit space endowed with a Lip-norm. We study morphisms and isomorphisms between compact quantum metric spaces. We give two sufficient conditions for a unital positive linear map of a compact quantum metric space with lower semicontinuous Lip-norm to be in fact a bi-Lipschitz map.


  • Botao LongDepartment of Mathematics
    MIIT Key Laboratory of Mathematical Modelling
    and High Performance Computing of Air Vehicles
    Nanjing University of Aeronautics and Astronautics
    Nanjing 211106, People’s Republic of China
  • Wei WuSchool of Mathematical Sciences
    Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice
    East China Normal University
    Shanghai 200241, People’s Republic of China

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