Satish Pandey, Department of Pure Mathematics, University of Waterloo
“Positive maps”
Having introduced the operator systems and positive maps from an operator system to an arbitrary C∗-algebra, we are prepared to develop some of the properties of positive maps. We shall be mainly concerned with how the assumptions of positivity is related to the norm of the map. The inequality ∥φ∥ ≤ 2∥φ(1)∥ for arbitrary positive maps on operator systems will subsequently be established and we will present at least two cases where ∥φ∥ = ∥φ(1)∥. As an application of these observations, we give a fairly elementary proof of von Neumann’s inequality and finally establish the celebrated theorem due to Russo-Dye.
MC 5403