Quantum metric spaces of quantum maps
Journal Title: Universal Journal of Mathematics and Applications (UJMA) - Year 2018, Vol 1, Issue 1
Abstract
We show that any quantum family of quantum maps from a noncommutative space to a compact quantum metric space has a canonical quantum pseudo-metric structure. Here by a 'compact quantum metric space' we mean a unital C*-algebra together with a Lipschitz seminorm, in the sense of Rieffel, which induces the weak* topology on the state space of the C*-algebra. Our main result generalizes a classical result to noncommutative world.
Authors and Affiliations
Maysam Maysami Sadr
Keywords
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