ICTS

If | \sum_{i,j=1}^n a_{i  j} s_i  t_j | is  less or equal to 1 for all  vectors s, t  with |s_i|, |t_i| less or equal to 1, then | \sum_{i,j}^n a_{i j} <x_i , y_j  > | less  or equal to K(n) for any choice of unit vectors x_1,..., ,x_n;  y_1,...,y_n in a Hilbert space H, 

The limit of  K(n)  remains  finite as  n  →  ∞  and is  the universal constant K  of Grothendieck. I will discuss this inequality along with many of its surprising consequences.