Journal Home Page Cumulative Index List of all Volumes Complete Contentsof this Volume Previous Article Journal of Convex Analysis 20 (2013), No. 3, 599--616Copyright Heldermann Verlag 2013 Strong Factorizations between Couples of Operators on Banach Function Spaces Olvido Delgado Dep. de Matemática Aplicada I, Universidad de Sevilla, Avenida Reina Mercedes s/n, 41012 Sevilla, Spain olvido@us.es Enrique A. Sánchez Pérez Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain easancpe@mat.upv.es [Abstract-pdf] Let $T\colon X_1\to Y_1$ and $S\colon X_2\to Y_2$ 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, $T=M_g\circ S\circ M_f$ with $M_f\colon X_1\to X_2$ and $M_g\colon Y_2\to Y_1$ 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. Keywords: Banach function spaces, factorization of operators, multiplication operators, product spaces, vector measures. MSC: 46E30, 47B38; 46B42 [ Fulltext-pdf  (196  KB)] for subscribers only.