Lower bounds of inner products in a real Hilbert spaces

Question

let $H$ be a real Hilbert space and let $x,y\in H$ such that the coordinates of the vectors $x$ and $y$ can be positive or negative, are there any theorems that deal with a lower bound of $<x,y>$? Is there a way to assure that $<x,y>\geqslant0$ (besides the trivial approach by which take the vectors $x$ and $y$ to be such that their coordinates are either all positive or either all negative) or $<x,y>\leqslant0$