ABSTRACT
Chapter 10
Lipschitz Algebras
10.1 The algebras Lip
(X)
The quantum version of a metric space is analogous to the quantum ver-
sions of topological and measure spaces. In each case there is a Hilbert
space generalization of the algebra of scalar-valued maps on such an ob-
ject which preserve the relevant structure. The topological and measure
theoretic categories involve the algebras C(X) and L
(X); in the metric
case the appropriate algebra is Lip
(X).
