Positive linear operator
Concept in functional analysis / From Wikipedia, the free encyclopedia
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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.
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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.