K-Theory of an Algebra of Pseudodifferential Operators on a Noncompact Manifold

Abstract

Let 𒜠denote the C*-algebra of bounded operators on L²(â„ × ð•Š¹) generated by: all multiplications a(M) by functions a â‹² C^∞(𕊹), all multiplications b(M) by functions b ⋲ C([−∞,+∞]), all multiplications by 2Ï€-periodic continuous functions, Λ = (1 − Δ_{â„×𕊹} )^−1/2, where Δ_{â„×𕊹} is the Laplacian operator on L²(â„ × ð•Š¹), and Ï‘_tΛ, Ï‘_xΛ, for t ⋲ â„ and x⋲ 𕊹. We compute the K-theory of 𒜠and of its quotient by the ideal of compact operators.