Factorization Theorems for Multiplication Operators on Banach Function Spaces

[EN] Let X Y and Z be Banach function spaces over a measure space . Consider the spaces of multiplication operators from X into the Kothe dual Y' of Y, and the spaces X (Z) and defined in the same way. In this paper we introduce the notion of factorization norm as a norm on the product space that is defined from some particular factorization scheme related to Z. In this framework, a strong factorization theorem for multiplication operators is an equality between product spaces with different factorization norms. Lozanovskii, Reisner and Maurey-Rosenthal theorems are considered in our arguments to provide examples and tools for assuring some requirements. We analyze the class of factorization norms, proving some factorization theorems for them when p-convexity/p-concavity type properties of the spaces involved are assumed. Some applications in the setting of the product spaces are given.The author was supported by the Ministerio de Econom´ıa y Competitividad (Spain) under grant #MTM2012-36740-C02-02.Sánchez Pérez, EA. (2014). Factorization Theorems for Multiplication Operators on Banach Function Spaces. Integral Equations and Operator Theory. 80(1):117-135. https://doi.org/10.1007/s00020-014-2169-11713580