Article
Factorizing operators on Banach function spaces through spaces of multiplication operators
Author/s | Calabuig, J. M.
Delgado Garrido, Olvido Sánchez Pérez, E. A. |
Department | Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII) |
Publication Date | 2010 |
Deposit Date | 2021-01-07 |
Published in |
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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 ... 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. |
Funding agencies | Generalitat Valenciana Ministerio de Educación y Ciencia (MEC). España |
Project ID. | TSGD-07
MTM2006-13000-C03-01 |
Citation | Calabuig, 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. |
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