If $\mathscr{F}$ is a normal filter on a regular uncountable cardinal $\kappa$, let $\|f\|$ be the $\mathscr{F}$-norm of an ordinal function $f$. We introduce the class of positive ordinal operations and prove that if $F$ is a positive operation then $\|F(f)\| \geq F(\|f\|)$. For each $\eta < \kappa^+$ let $f_\eta$ be the canonical $\eta$th function. We show that if $F$ is a $\Sigma$ operation then $F(f_\eta) = f_{F(\eta)}$. As an application we show that if $\kappa$ is greatly Mahlo then there are normal filters on $\kappa$ of order greater than $\kappa^+$.