Orbits of Positive Operators from a Differentiable Viewpoint

Abstract

Let A be a unital C*-algebra and G the group of units of A. A geometrical study of the action of G over the set A^+ of all positive elements of A is presented. The orbits of elements with closed range by this action are provided with a structure of differentiable homogeneous space with a natural connection. The orbits are partitioned in "components" which also have a rich geometrical structure