Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9495873 | Journal of Functional Analysis | 2005 | 26 Pages |
Abstract
Consider a vector measure of bounded variation m with values in a Banach space and an operator T:Xâ¶L1(m), where L1(m) is the space of integrable functions with respect to m. We characterize when T can be factorized through the space L2(m) by means of a multiplication operator given by a function of L2(|m|), where |m| is the variation of m, extending in this way the Maurey-Rosenthal Theorem. We use this result to obtain information about the structure of the space L1(m) when m is a sequential vector measure. In this case the space L1(m) is an â-sum of L1-spaces.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
A. Fernández, F. Mayoral, F. Naranjo, C. Sáez, E.A. Sánchez-Pérez,