Quantum metric spaces of quantum maps

Authors : Maysam MAYSAMİ SADR

Pages : 54-60

Doi:10.32323/ujma.382008

View : 101 | Download : 11

Publication Date : 2018-03-11

Article Type : Research Paper

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

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