Infinite dimensional extension of A.P. Calderon's theorem on positive semidefinite biquadratic forms

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

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