Infinite dimensional extension of A. P. Calderón's theorem on positive semidefinite biquadraric forms

We extend to the infinite dimensional separable real Hilbert spaces a theorem of A. P. Calderón which says that, if $m=2$ or $n=2$, then every positive semidefinite biquadratic form on $\mathbf R^m\times\mathbf R^n$ is a sum of squares of bilinear forms.