Grothendieck inequality
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In mathematics, the Grothendieck inequality relates
to
,
where B(H) is the unit ball of a Hilbert space H. The best constant k(H) in
is called the Grothendieck constant of the Hilbert space H.
Alexander Grothendieck showed that k(H) is bounded by a universal constant, independent of H; define
Grothendieck himself proved that
Later, Krivine showed that
in spite of later efforts, the precise value of k is still unknown.
[edit] References
- A.Grothendieck, Résumé de la théorie métrique des produits tensoriels topologiques (French), Bol. Soc. Mat. São Paulo 8 1953 1--79
- J.-L. Krivine, Constantes de Grothendieck et fonctions de type positif sur les spheres., Adv. Math. 31, 16-30, 1979.
[edit] External links
- Eric W. Weisstein, Grothendieck's Constant at MathWorld. (NB: the historical part is not exact there)
