Graded C*-algebras associated to symplectic spaces and spectral analysis of many channel hamiltonians

In the first part of this paper we associate a C*-algebra of pseudo-differential operators to each finite, sup-stalbe family of subspaces of a symplectic space; the hamiltonians usually consisered in the N-body problem are affiliated to such algebras. Then we present a purely algebraic approach to the spectral theory of these hamiltonians, in particular a C*-algebra version of Mourre theory. Finally, we give a new proof of the Mourre estimate, which does not involve any geometric object (such as partitions of unity in configuration space). (orig.)