= Positive linear operator on continuous functions
{title2=$f\geq0\Rightarrow Uf\geq0$}
= Positive linear operators on continuous functions
{synonym}
A linear map $U:C(K,\mathbb R)\to C(K,\mathbb R)$ is positive when $f\geq0$ implies $Uf\geq0$. This is positivity for the pointwise order, not positivity of a quadratic form. On a compact space, $|Uf|\leq U|f|\leq\|f\|_\infty U1$, so $\|U\|=\|U1\|_\infty$. This makes positive maps especially useful for <uniform approximation>.
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