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Journal of Convex Analysis 20 (2013), No. 3, 599--616
Copyright 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

Enrique A. Sánchez Pérez
Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain


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

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