Strong Factorizations between Couples of Operators on Banach Function Spaces

[EN] 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.The research of the first author has been partially supported by MTM2012-36732-C03-03 (Ministerio de Economia y Competitividad, Spain), FQM-262, FQM-4643, FQM-7276 (Junta de Andalucia) and Feder Funds (European Union). The research of the second author has been supported by MTM2012-36740-C02-02 (Ministerio de Economia y Competitividad, Spain).Delgado Garrido, O.; Sánchez Pérez, EA. (2013). Strong Factorizations between Couples of Operators on Banach Function Spaces. Journal of Convex Analysis. 20(3):599-616. http://hdl.handle.net/10251/4901959961620