The natural functions in this context are Lipschitz; e.g. functions $d_x(y)=d(x,y)$ determine an isometric embedding of a metric space $X$ to $L_\infty(X)$. For a noncommutative analogue see G.Kuperberg, N.Weaver, "A von Neumann algebra approach to quantum metrics", https://arxiv.org/abs/1005.0353
Misha
- 31.2k
- 1
- 94
- 163