Polynomial approximation of quantum Lipschitz functions

TL;DR

This paper demonstrates that Lipschitz functions on the quantum sphere can be approximated effectively, establishing that two natural quantum metric structures on the quantum sphere are indistinguishable in the quantum Gromov-Hausdorff sense.

Contribution

It introduces a polynomial approximation result for quantum Lipschitz functions, showing the equivalence of two quantum metric structures on the quantum sphere.

Findings

Quantum Lipschitz functions can be approximated by polynomials.

The two quantum metric structures on $S_q^2$ have quantum Gromov-Hausdorff distance zero.

The result bridges classical approximation theory and quantum metric geometry.

Abstract

We prove an approximation result for Lipschitz functions on the quantum sphere $S_q^2$, from which we deduce that the two natural quantum metric structures on $S_q^2$ have quantum Gromov-Hausdorff distance zero.