Standard generalized vectors and ∗-automorphism groups of partial O∗-algebras

It is known that standard generalized vectors on a partial O∗-algebra M provide a way of constructing (generalized) KMS states on M, via the Tomita-Takesaki theory of modular automorphisms. Such states represent equilibrium states if M is the observable set of some physical system. In this paper we discuss a simplified form of these standard generalized vectors, called natural, characterized by the fact that they have a core consisting of universal right multipliers. We also investigate the interplay between the ∗-automorphism groups generated by two standard generalized vectors λ and μ, on M. When M is a self-adjoint partial GW∗-algebra, we prove the existence of the Connes cocycle [Dμ: Dλ] and we establish a Radon-Nikodym theorem, generalizing that obtained by Pedersen and Takesaki for a von Neumann algebra.