Abstract
We show that the noncommutative differential geometry of quantum projective spaces is compatible with Rieffel's theory of compact quantum metric spaces. This amounts to a detailed investigation of the Connes metric coming from the unital spectral triple introduced by D'Andrea and Dąbrowski. In particular, we establish that the Connes metric metrizes the weak-⁎ topology on the state space of quantum projective space. This generalizes previous work by the second author and Aguilar regarding spectral metrics on the standard Podleś spheres.
Originalsprog | Engelsk |
---|---|
Artikelnummer | 110466 |
Tidsskrift | Journal of Functional Analysis |
Vol/bind | 287 |
Udgave nummer | 2 |
Antal sider | 38 |
ISSN | 0022-1236 |
DOI | |
Status | Udgivet - 15. jul. 2024 |