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.
Compact quantum metric space C*-algebra Lipschitz algebra Quantum family of maps State space
Primary Language | English |
---|---|
Subjects | Mathematical Sciences |
Journal Section | Articles |
Authors | |
Publication Date | March 11, 2018 |
Submission Date | January 21, 2018 |
Acceptance Date | February 28, 2018 |
Published in Issue | Year 2018 |
Universal Journal of Mathematics and Applications
The published articles in UJMA are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.