Definition:Parametric Operator

Definition
Let $A$ be an index set.

Let $\Omega$ be a indexed family of operators $\left({\Omega_{\alpha} }\right)_A = \left\{ {\Omega_\alpha: \alpha \in A}\right\}$ indexed by the index $\alpha$.

Then $\Omega$ is a parametric operator with parameter $\alpha$ in the parameter set $A$.