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http://cimat.repositorioinstitucional.mx/jspui/handle/1008/876| Strong factorization of operators on spaces of vector measure integrable functions and unconditional convergence of series | |
| FERNANDO GALAZ FONTES | |
| Acceso Abierto | |
| Atribución-NoComercial-CompartirIgual | |
| Factorización | |
| In this paper, we characterize the space of multiplication operators from an Lp-space into a space L1(m) of integrable functions with respect to a vector measure m, as the subspace L1 p,μ(m) of L1(m) defined by the functions that have finite p-semivariation. We prove several results concerning the Banach lattice structure of such spaces. We obtain positive results—for instance, they are always complete, and we provide counterexamples to prove that other properties are not satisfied—for example, simple functions are not in general dense. We study the operators that factorize through L1 p,μ(m), and we prove an optimal domain theorem for such operators. We use our characterization to generalize the Bennet–Maurey–Nahoum Theorem on decomposition of functions that define an unconditionally convergent series in L1[0, 1] to the case of 2-concave Banach function spaces. | |
| Springer Verlag | |
| 2007 | |
| Artículo | |
| Inglés | |
| Investigadores | |
| OTRAS | |
| Versión publicada | |
| publishedVersion - Versión publicada | |
| Aparece en las colecciones: | Matemáticas |
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