Abstract
Based on operators borrowed from scattering theory, several concrete realizations of index theorems will be presented. The corresponding operators belong to some C*algebras of pseudo-differential operators with coefficients which either have limits at + or - infinity, or which are periodic or asymptotically periodic, or which are uniformly almost periodic. These various situations can be deduced from a single partial isometry which depends on several parameters. From a different point of view, these investigations correspond to a Levinson’s type theorem when an infinite number of bound states is involved.