On the structure of the essential spectrum of elliptic operators on metric spaces

We give a description of the essential spectrum of a large class of operators on metric measure spaces in terms of their localizations at infinity. These operators are analogues of the elliptic operators on Euclidean spaces and our main result concerns the ideal structure of the $C^*$-algebra generated by them.Comment: Improved presentation, some new results

On the Spectral Analysis of Quantum Field Hamiltonians

We define C*-algebras on a Fock space such that the Hamiltonians of quantum field models with positive mass are affiliated to them. We describe the quotient of such algebras with respect to the ideal of compact operators and deduce consequences in the spectral theory of these Hamiltonians: we compute their essential spectrum and give a systematic procedure for proving the Mourre estimate