Factorizing operators on Banach function spaces through spaces of multiplication operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:364

Article

Calabuig, J. M.¹  Delgado, O.¹  Sanchez Perez, E. A.¹ 

[1] Univ Politecn Valencia, Inst Univ Matemat Pura & Aplicada, Valencia 46022, Spain

关键词: Banach function spaces;    Factorization of operators;    Multiplication operators;    Vector measures;   

DOI  :  10.1016/j.jmaa.2009.10.034

来源: Elsevier

【 摘 要 】

In order to extend the theory of optimal domains for continuous operators on a Banach function space X(mu) over a finite measure mu, 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 mu and the measure defined by the operator T and, by using delta-rings, mu 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. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free