2021-01-072021-01-072010Calabuig, J.M., Delgado Garrido, O. y Sánchez Pérez, E.A. (2010). Factorizing operators on Banach function spaces through spaces of multiplication operators. Journal of Mathematical Analysis and Applications, 364 (1), 88-103.0022-247Xhttps://hdl.handle.net/11441/103436In order to extend the theory of optimal domains for continuous operators on a Banach function space X(μ) over a finite measure μ, we consider operators T satisfying other type of inequalities than the one given by the continuity which occur in several well-known factorization theorems (for instance, Pisier Factorization Theorem through Lorentz spaces, pth-power factorable operators . . . ). We prove that such a T factorizes through a space of multiplication operators which can be understood in a certain sense as the optimal domain for T . Our extended optimal domain technique does not need necessarily the equivalence between μ and the measure defined by the operator T and, by using δ-rings, μ is allowed to be infinite. Classical and new examples and applications of our results are also given, including some new results on the Hardy operator and a factorization theorem through Hilbert spaces.application/pdf16engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Banach function spacesFactorization of operatorsMultiplication operatorsVector measuresinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1016/j.jmaa.2009.10.034