The final publication is available at Springer via http://dx.doi.org/10.1007/s00009-014-0384-3[EN] In this paper, we characterize compact linear operators from
Banach function spaces to Banach spaces by means of approximations
with bounded homogeneous maps. To do so, we undertake a detailed
study of such maps, proving a factorization theorem and paying special
attention to the equivalent strong domination property involved. Some
applications to compact maximal extensions of operators are also given.The authors thank the referee for his/her careful revision and suggestions. The first author gratefully acknowledges the support of the Ministerio de Economia y Competitividad (Spain), under Project #MTM2011-22417. The second author gratefully acknowledges the support of the Ministerio de Economia y Competitividad (Spain), under Project #MTM2012-36740-c02-02.Rueda, P.; Sánchez Pérez, EA. (2015). Factorization theorems for homogeneous maps on banach function spaces and approximation of compact operators. Mediterranean Journal of Mathematics. 12(1):89-115. https://doi.org/10.1007/s00009-014-0384-3S89115121Calabuig J.M., Delgado O., Sánchez Pérez E.A.: Factorizing operators on Banach function spaces through spaces of multiplication operators. J. Math. Anal. Appl. 364, 88–103 (2010)Defant, A.: Variants of the Maurey–Rosenthal theorem for quasi Köthe function spaces. Positivity 5, 153–175 (2001)Delgado, O., Sánchez Pérez, E.A.: Strong factorizations between couples of operators on Banach spaces, J. Conv. Anal. 20(3), 599–616 (2013)Diestel, J., Uhl, J.J.: Vector measures, Math. Surv. vol. 15, Amer. Math. Soc., Providence (1977)Fernández A., Mayoral F., Naranjo F., Sáez C., Sánchez-Pérez E.A.: Spaces of p-integrable functions with respect to a vector measure. Positivity 10, 1–16 (2006)Ferrando I., Rodríguez J.: The weak topology on L p of a vector measure. Topol. Appl. 155(13), 1439–1444 (2008)Lindenstrauss, J., Tzafriri, L.: Classical Banach Spaces, II, Springer, Berlin (1996)Maligranda L., Persson L.E.: Generalized duality of some Banach function spaces. Indag. Math. 51, 323–338 (1989)Meyer-Nieberg, P.: Banach lattices, Springer, Berlin (1991)Okada, S.: Does a compact operator admit a maximal domain for its compact linear extension? In: Vector measures, integration and related topics. Operator theory: advances and applications, Vol. 201, pp. 313–322. Birkhäuser, Basel (2009)Okada S., Ricker W.J., Rodríguez-Piazza L.: Compactness of the integration operator associated with a vector measure. Studia Math. 150(2), 133–149 (2002)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal domain and integral extension of operators acting in function spaces. Operator theory: advances and applications, 180. Birkhäuser, Basel (2008)Sánchez Pérez, E.A.: Compactness arguments for spaces of p-integrable functions with respect to a vector measure and factorization of operators through Lebesgue–Bochner spaces, Illinois J. Math. 45(3), 907–923 (2001
