  Universal continuous calculi are defined and it is shown that for every
finite tuple of pairwise commuting Hermitian elements of a Su*-algebra (an
ordered *-algebra that is symmetric, i.e. "strictly" positive elements are
invertible, and uniformly complete), such a universal continuous calculus
exists. This generalizes the continuous calculus for C*-algebras to a class of
generally unbounded ordered *-algebras. On the way, some results about
*-algebras of continuous functions on locally compact spaces are obtained. The
approach used throughout is rather elementary and especially avoids any
representation theory.
