- Universal Journal of Mathematics and Applications
- Vol: 1 Issue: 1
- Quantum metric spaces of quantum maps
Quantum metric spaces of quantum maps
Authors : Maysam Maysami Sadr
Pages : 54-60
Doi:10.32323/ujma.382008
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Publication Date : 2018-03-11
Article Type : Research
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.Keywords : Compact quantum metric space, C*-algebra, Lipschitz algebra, Quantum family of maps, State space