On characterizations of commutativity of C*-algebras

Abstract

We give three kinds of characterizations of the commutativity of C ∗ ^* - algebras. The first is the one from operator monotone property of functions regarded as the nonlinear version of Stinespring theorem, the second one is the characterization of commutativity of local type from expansion formulae of related functions and the third one is of global type from multiple positivity of those nonlinear positive maps induced from functions.