Strictly singular multiplication operators on L(X)

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

Pedro Tradacete (ICMAT Madrid)


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 LARB acting on L(X) as LARB(T)= ATB. The general aim is to study properties of LARB in terms of those of A and B. In particular, Lindström, Saksman and Tylli in 2005 have shown that, when X=Lp, the multiplication LARB 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 Lp then LARB actually factors through the space compact operators on the sequence space lp. This is based on joint work with M. Mathieu.

Mathematical Sciences Research Centre