AG Mathematische Physik, Ian Koot (FAU): The propagation number of operator systems

Ian Koot (FAU)

The propagation number of operator systems

Abstract:
It is well known that every C*-algebra is isomorphic to a norm-closed, self-adjoint subalgebra of the bounded operators on some Hilbert space. We can generalize this to norm-closed, self-adjoint subspaces of bounded operators; these structures are called operator systems. The spectral triple-formulation of Noncommutative Geometry is based on C*-algebras, and in their recent efforts to generalize this to operator systems, Connes and Van Suijlekom defined a property of operator systems which they called the propagation number. We invastigate the behaviour of the propagation number under the minimal tensor product of operator systems, where an exact expression for the propagation number of the tensor product in terms of the propagation number of its factors can be found. We also discuss the possibility of an expression for the propagtion number of the dual operator system.