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• W2020755220 abstract "In 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." @default.
• W2020755220 created "2016-06-24" @default.
• W2020755220 creator A5022826124 @default.
• W2020755220 creator A5058079445 @default.
• W2020755220 creator A5059955897 @default.
• W2020755220 date "2010-04-01" @default.
• W2020755220 modified "2023-10-06" @default.
• W2020755220 title "Factorizing operators on Banach function spaces through spaces of multiplication operators" @default.
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• W2020755220 doi "https://doi.org/10.1016/j.jmaa.2009.10.034" @default.
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