Definition:Continuous Linear Transformation Space

Definition

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 $\map C {X, Y}$ be the continuous mapping space.

Then $\map {CL} {X, Y}$ is the continuous linear transformation space defined as:

$\map {CL} {X, Y} := \map C {X, Y} \cap \map \LL {X, Y}$