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 _{A}R_{B}* acting on

*L*(

*X*) as

*L*(

_{A}R_{B}*T*)=

*ATB*. The general aim is to study properties of

*L*in terms of those of

_{A}R_{B}*A*and

*B*. In particular, Lindström, Saksman and Tylli in 2005 have shown that, when

*X*=

*L*, the multiplication

_{p}*L*is strictly singular precisely when

_{A}R_{B}*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*then

_{p}*L*actually factors through the space compact operators on the sequence space

_{A}R_{B}*l*. This is based on joint work with M. Mathieu.

_{p}