Subspaces of ${\mathrm{\ell }}_1$ satisfying Grothendieck's theorem

We characterize the subspaces $X$ of ${\mathrm{\ell }}_1$ satisfying Grothendieck’s theorem in terms of extension of nonnegative quadratic forms $q:X⟶\mathbb{R}$ to the whole ${\mathrm{\ell }}_1$.