Quantum metric spaces of quantum maps

Year 2018, Volume: 1 Issue: 1, 54 - 60, 11.03.2018

Maysam Maysami Sadr

https://doi.org/10.32323/ujma.382008

Cited By: 2

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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