Given a smooth projective variety $X \subset \Bbb{CP}^k$ why is it true that global sections of $O(l)|_X, l >0 $ are just global sections of $O(l)$ on $\Bbb{CP}^k$ restricted to $X$?

Here $O(l)$ is just an appropriate power of the canonical line bundle on $\Bbb{CP}^k$.

Given a smooth projective variety $X \subset \Bbb{CP}^k$ why is it true that global sections of $O(l)|_X, l >> 0 $ are just global sections of $O(l)$ on $\Bbb{CP}^k$ restricted to $X$?

Here $O(l)$ is just an appropriate power of the anti-tautological line bundle on $\Bbb{CP}^k$.