On representations of Ψ* andC *-algebras ofb-pseudo-differential operators on manifolds with corners

Abstract

The author computes the Jacobson topology and the corresponding Borel structure on the spectrum of\(B(Z,{}^b\Omega ^{\tfrac{1}{2}} )\). Here\(B(Z,{}^b\Omega ^{\tfrac{1}{2}} )\) denotes the C*-algebra generated by the algebra\(\Psi _{b,cl}^0 B(Z,{}^b\Omega ^{\tfrac{1}{2}} )\) of b-pseudo-differential operators of orderO on a compact manifold with corners (in the sense of Melrose). The author also reduces the problem of classification of representations to the problem of classification of positive Borel measures on certain well-known Borel spaces. Bibliography:29 titles.