Sequences of operator algebras converging to odd spheres in the quantum Gromov–Hausdorff distance

Abstract

Marc Rieffel had introduced the notion of the quantum Gromov–Hausdorff distance on compact quantum metric spaces and found a sequence of matrix algebras that converges to the space of continuous functions on 2-sphere in this distance. One finds applications of similar approximations in many places in the theoretical physics literature. In this paper, we have defined a compact quantum metric space structure on the sequence of Toeplitz algebras on generalized Bergman spaces and have proved that the sequence converges to the space of continuous functions on odd spheres in the quantum Gromov–Hausdorff distance.