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

Antoine, Jean-Pierre [UCL] Inoue, A. Ogi, H.

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 lambda and mu on M. When M is a self-adjoint partial GW*-algebra, we prove the existence of the Comes cocycle [D mu : D lambda] and we establish a Radon-Nikodym theorem, generalizing that obtained by Pedersen and Takesaki for a von Neumann algebra.