Gelfand theory of certain \(C^*\)-algebras on nonasymptotically flat manifolds (Q1113062)

The author considers a certain \(C^*\)-algebra of zero-order pseudo- differential operators on a complete Riemannian manifold with finitely many conical ends. He identifies the commutator ideal (it turns out to be the compact operators), the maximal ideal space of the commutative quotient, and the corresponding Gelfand map. For first-order differential operators ``within reach'' he gives a necessary and sufficient Fredholm condition. We refer to \textit{H. O. Cordes} [Spectral theory of linear differential operators and comparison algebras, Lond. Math. Soc. Lect. Notes Ser. 76 (1987)] for the general background of methods.