About: Positive linear operator

In mathematics, more specifically in functional analysis, a positive linear operator from an preordered vector space into a preordered vector space is a linear operator on into such that for all positive elements of that is it holds that In other words, a positive linear operator maps the positive cone of the domain into the positive cone of the codomain. Every positive linear functional is a type of positive linear operator. The significance of positive linear operators lies in results such as Riesz–Markov–Kakutani representation theorem.