\begin{definition}[Definition:Continuous Linear Transformation Space]
Let $K$ be a field.
Let $X, Y$ be normed vector spaces over $K$.
Let $\map \LL {X, Y}$ be the set of all linear transformations.
Let $\map \CC {X, Y}$ be the continuous mapping space.
Then $\map {CL} {X, Y}$ is the '''continuous linear transformation space''' defined as:
:$\map {CL} {X, Y} := \map \CC {X, Y} \cap \map \LL {X, Y}$
\end{definition}