Colloquium: Bad Student Matrix Products Using Singular Integrals

Abstract: A Schur multiplier S_M is a linear operator associated to a matrix M=[m_{i,j}]_{i,j}, called its symbol. It acts on other matrices by entrywise multiplication, that is,

S_M(A) = [m_{i,j}a_{i,j}]_{i,j}, \quad A=[a_{i,j}]_{i,j}.

The boundedness of Schur multipliers in the Schatten-von Neumann classes is an interesting question in operator algebra that was already considered by Grothendieck. We will explain how smoothness of the symbol M --seen as a function of two variables-- is key to finding sufficient conditions for the boundedness of the corresponding Schur multiplier and other operators of the same flavor. This will come from a surprising connection with Fourier multipliers and noncommutative Calderón-Zygmund theory. Based on joint works with Adrián M. González Pérez, Javier Parcet and Eduardo Tablate.

Host: Brett Wick

Reception to follow at Cupples I, Room 200 (Lounge) from 2:00pm to 3:00pm