On the ergodic power function for invertible positive operators
We first study positivity in C*-modules using tripotents ( = partial isometries) which are what we call open. This is then used to study ordered operator spaces via an "ordered noncommutative Shilov boundary" which we introduce. This boundary satisfies the usual universal diagram/property of the noncommutative Shilov boundary, but with all the arrows completely positive. Because of their independent interest, we also systematically study open tripotents and their properties.
The aim of this paper is to develop a theory of p-summing operators (between Banach spaces) in presence of an order structure given by a convex normal cone.