Spectral metrics on quantum projective spaces

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.