Abstract
Let T : X1 --> Y1 and S : X2 --> Y2 be two continuous linear operators between Banach function
spaces related to a finite measure space. Under some lattice requirements on the spaces involved,
we give characterizations by means of inequalities of when T can be strongly factorized through
S, that is, T = Mg S Mf with Mf : X1 --> X2 and Mg : Y2 --> Y1 being multiplication operators
defined by some measurable functions f and g. In particular, we study the cases when S is a
composition operator or a kernel operator.
