Haagerup's proof of the non commutative little Grothendieck inequality raises some questions on the commutative little inequality, and it offers a new result on scalar matrices with non negative entries. The theory of completely bounded maps implies that the commutative Grothendieck inequality follows from the little commutative inequality, and that this passage may be given a geometric form as a relation between a pair of compact convex sets of positive matrices, which, in turn, characterizes the little constant in the complex case.

翻译：Haagerup对非交换小Grothendieck不等式的证明引发了对交换小不等式的若干问题，并给出了关于非负元素标量矩阵的新结果。完全有界映射理论表明，交换Grothendieck不等式可由小交换不等式推导得出，且这一过渡可赋予几何形式，表现为正矩阵的一对紧凸集之间的某种关系，而这种关系实际上刻画了复情形下的小常数。