Lipschitz isometries of compact quantum metric spaces
Journal of Mathematical Analysis and Applications(2020)
摘要
A compact quantum metric space is a complete order unit space endowed with a Lip-norm. We investigate the category morphism between compact quantum metric spaces. We show that a unital positive linear map between compact quantum metric spaces with lower semicontinuous Lip-norms is Lipschitz if and only if it preserves the Lipschitz elements. We characterize when a unital positive linear map on a compact quantum metric space with lower semicontinuous Lip-norm is a Lipschitz isometry.
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关键词
Compact quantum metric space,Lip-norm,Lipschitz morphism,Asymptotically nonexpansive map,Asymptotically expansive map,Lipschitz isometry
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