Prove a lower bound of the smooth convex function with Lipschitz continuous gradient

Question

how to prove this conclusion:

Suppose that $f$ is a smooth convex function with Lipschitz continuous gradient on $X$, then there exists a self-adjoint and positive semi-definite linear operators $\sum_{f}$ such that for any $x, x^{'}\in X$, $$f(x)\geq f(x') + \langle x -x', \nabla f(x')\rangle + 0.5 *\|x-x'\|_{\sum_{f}}^2.$$

Thanks for your attention and response.

Answer 1

What about the function $f(x) = 0$ !!!