Factorizing operators on Banach function spaces through spaces of multiplication operators |
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Authors: | J.M. Calabuig,E.A. Sá nchez Pé rez |
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Affiliation: | Instituto Universitario de Matemática Pura y Aplicada, Universitat Politècnica de València, València 46022, Spain |
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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. |
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Keywords: | Banach function spaces Factorization of operators Multiplication operators Vector measures |
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