# Journal of Operator Theory

Volume 34, Issue 2, Fall 1995 pp. 263-283.

Grothendieck type norms for bilinear forms on C*-algebras**Authors**: Uffe Haagerup (1) and Takashi Itoh (2)

**Author institution:**(1) Institut for Matematik og Datalogi, Odense Universitet, DK-5230 Odense M, DENMARK

(2) Department of Mathematics, Gunma University, Aramaki, Maebashi, 371, JAPAN

**Summary:**We consider three equivalent norms on the space Bil(A, B) of bilinear forms on a pair of C*-algebras (A, B), namely the usual norm and two norms (here denoted \left\| \cdot \right\|_{{\rm{J*}}} and \left\| \cdot \right\|_{{\rm{tb*}}}) related to the non-commutative Grothendieck inequality and to completely bounded maps from A to B*. The two latter norms were introduced by Blecher and the second named author some years ago. We show that the three norms are mutually distinct, and give estimates of the best constants in the comparison of these norms.

**Keywords:**C*-algebra, non-commutative Grothendieck inequality, Kneser graph.

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