This paper is about
a C∗-algebra A of 0-order pseudo-differential operators on L2(Ω), where
Ω is a complete Riemannian manifold which need not be compact. This
algebra is designed to handle singular elliptic theory for certain N-th-order
differential operators. In particular, this paper studies the maximal ideal
space M of the (commutative) algebra A∕𝒦, where 𝒦 denotes the compact
ideal. The space M contains the bundle of cospheres as a subspace, and
in general will contain additional points at infinity of the manifold. The
significance of this for elliptic theory lies in the fact that an operator A ∈ A is
Fredholm if and only if the associated continuous function σA∈ C(M) is never
zero.
