Geodesic
Infinite dimensional extension of A.\,P.~Calder\'on's theorem on positive semidefinite biquadraric forms
Lobachevskii journal of mathematics, Tome 10 (2002), pp. 3-8.

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Keywords: biquadratic form, positive operator, Hilbert–Schmidt operator. 
@article{LJM_2002_10_a0,
     author = {B. Aqzzouz and M. Kadiri},
     title = {Infinite dimensional extension of {A.\,P.~Calder\'on's} theorem on positive semidefinite biquadraric forms},
     journal = {Lobachevskii journal of mathematics},
     pages = {3--8},
     publisher = {mathdoc},
     volume = {10},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2002_10_a0/}
}
TY  - JOUR
AU  - B. Aqzzouz
AU  - M. Kadiri
TI  - Infinite dimensional extension of A.\,P.~Calder\'on's theorem on positive semidefinite biquadraric forms
JO  - Lobachevskii journal of mathematics
PY  - 2002
SP  - 3
EP  - 8
VL  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2002_10_a0/
LA  - en
ID  - LJM_2002_10_a0
ER  - 
%0 Journal Article
%A B. Aqzzouz
%A M. Kadiri
%T Infinite dimensional extension of A.\,P.~Calder\'on's theorem on positive semidefinite biquadraric forms
%J Lobachevskii journal of mathematics
%D 2002
%P 3-8
%V 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2002_10_a0/
%G en
%F LJM_2002_10_a0
B. Aqzzouz; M. Kadiri. Infinite dimensional extension of A.\,P.~Calder\'on's theorem on positive semidefinite biquadraric forms. Lobachevskii journal of mathematics, Tome 10 (2002), pp. 3-8. http://geodesic.mathdoc.fr/item/LJM_2002_10_a0/

[1] A. P. Calderón, “A note on biquadratic forms”, Linear Algebra Appl., 7 (1973), 175–177 | DOI | MR | Zbl

[2] M.-D. Choi, “Positive semidefinite biquadratic forms”, Linear Algebra Appl., 12 (1975), 95–100 | DOI | MR | Zbl

[3] M. El Kadiri, “Sur les génératrices extrémales de certains cônes de formes quadratiques doublement positives”, C. R. Acad. Sci. Paris, Ser. I, 324 (1997), 421–425 | MR | Zbl

[4] M. El Kadiri, “Opérateurs positifs sur certains espaces de formes quadratiques”, Linear Algebra Appl., 283 (1998), 273–288 | DOI | MR | Zbl