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

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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.


Proof

Take $Y = X$ in Necessary and Sufficient Conditions for Continuous Linear Transformation Space to be Banach Space.


$\blacksquare$


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