Nuclear maps and modular structures. Pt. 2

A correspondence between spectral properties of modular operators appearing in quantum field theory and the Hamiltonian is established. It allows to prove the 'distal' split property for a wide class of models. Conversely, any model having this property is shown to satisfy the Haag-Swieca compactness criterion. The results lead to a new type of nuclearity condition which can be applied to quantum field theories on arbitrary space-time manifolds. (orig.)