Necessary and Sufficient Conditions for Continuous Linear Transformation Space to be Banach Space/Corollary 2

Theorem
Let $\struct {X, \norm {\, \cdot \,}_X}$ be a Banach space.

Let $CL$ be the continuous linear transformation space.

Let $\norm {\, \cdot \,}$ be the supremum operator norm.

Then $\struct {\map {CL} {X, X}, \norm{\, \cdot \,}}$ is a Banach space.