Quantum metrics on noncommutative spaces

Abstract

We introduce two new algebraic formulations for the notion of 'quantum metric on noncommutative space'. For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the C*-algebra with itself. We consider some basic properties of these new objects, and state some connections with the Rieffel theory of compact quantum metric spaces.