Chennai Mathematical Institute


3.30-4.30 p.m., Seminar Hall
R.K. Rubugunday Distinguished Lecture
The Grothendieck inequality

Gadadhar Misra
IISc, Bangalore.


The Grothendieck inequality asserts the existence of an universal constant K with the property: If A is an n by n matrix with | \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} | less or equal to K(n). for any choice of unit vectors x_1,..., x_n; y_1,...,y_n of a Hilbert space H, The limit of K(n) remains finite as n -> \infty and is the universal constant K of Grothendieck. We will discuss this inequality along with many of its surprising consequences.