Change this paragraph to be clearer.
One composes with the injection of C (( 0, 1) ) into L (( 0, 1) ). One sees that T acts compactly from L (( 0, 1) ) to itself.
Composing with the injection of C (( 0, 1) ) into L (( 0, 1) ), one sees that T acts compactly from L (( 0, 1) ) to itself.