The Archimedean Property

The central notion in Chapter 5 is the Archimedean property, the single most important result is the Archimedean positivstellensatz. Major applications are given to polynomials that are strictly positive on some domain, such as the positivstellensätze of Schmüdgen and Putinar. An optional alternative approach is offered, which uses pure states for convex cones and leads to the Archimedean local-global principle.