24/05/2019, 14:00 - 15:00 in MAP/0G/018

Pedro Tradacete (ICMAT Madrid)

Abstract:

For a Banach space X, let L(X) denote the space of bounded linear operators from X to itself. For any pair of operators A,B in L(X) one can define the multiplication operator L_AR_B acting on L(X) as L_AR_B(T)= ATB. The general aim is to study properties of L_AR_B in terms of those of A and B. In particular, Lindström, Saksman and Tylli in 2005 have shown that, when X=L_p, the multiplication L_AR_B is strictly singular precisely when A and B are. The proof is however undesirably lengthy. In this talk, we will see a factorization argument which could provide an alternative approach: if A and B are strictly singular on L_p then L_AR_B actually factors through the space compact operators on the sequence space l_p. This is based on joint work with M. Mathieu.