On Orientation and Dynamics in Operator Algebras.¶Part I

Abstract:

This paper characterizes the self-adjoint part of C*-algebras and von Neumann algebras among normed Jordan algebras. It also explains how the associative product is determined by a general notion of orientation which is related to dynamics and reflects the dual role of physical variables as observables and as generators of one-parameter groups of motions of the state space (Schrödinger picture). This concept of orientation bridges the approach in Connes' characterization of the natural cone of a von Neumann algebra and our own characterization of the state space of a C*-algebra.