Geodesic
Strong Factorizations between Couples of Operators on Banach Function Spaces
Journal of convex analysis, Tome 20 (2013) no. 3, pp. 599-616

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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.
Classification : 46E30, 47B38, 46B42
Mots-clés : Banach function spaces, factorization of operators, multiplication operators, product spaces, vector measures 
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     author = {O. Delgado and E. A. S\'anchez P\'erez},
     title = {Strong {Factorizations} between {Couples} of {Operators} on {Banach} {Function} {Spaces}},
     journal = {Journal of convex analysis},
     pages = {599--616},
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     year = {2013},
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O. Delgado; E. A. Sánchez Pérez. Strong Factorizations between Couples of Operators on Banach Function Spaces. Journal of convex analysis, Tome 20 (2013) no. 3, pp. 599-616. http://geodesic.mathdoc.fr/item/JCA_2013_20_3_JCA_2013_20_3_a0/