I am really struggling here so i hope you can help me out.
Let $X_1 , X_2, Y$ be normed Vectorspaces and $L(X_1,X_2)$ be the vectorspace of continuous linear functions.
Show that
$\Phi: L(X_1,L(X_2,Y)) \longrightarrow L(X_2,L(X_1,Y)) \quad \text{with} \quad \Phi(A)x_1 := (x_2\longrightarrow A(x_2)x_1) $
is a norm preserving isomorphism.