Vector measure Maurey–Rosenthal-type factorizations and -sums of -spaces |
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| Authors: | A Fernndez F Mayoral F Naranjo C Sez EA Snchez-Prez |
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| Institution: | aDpto. Matemática Aplicada II, Escuela Técnica Superior de Ingenieros, Universidad de Sevilla, Camino de los Descubrimientos, s/n, 41092-Sevilla, Spain;bDpto. Matemática Aplicada II, Escuela Universitaria Politécnica, Virgen de África, 7, 41011-Sevilla, Spain;cDpto. de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera, 14, 46022-Valencia, Spain |
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| Abstract: | Consider a vector measure of bounded variation m with values in a Banach space and an operator T:XL1(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 ℓ-sum of L1-spaces. |
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| Keywords: | Vector measures p-Integrable functions Factorizations of operators ℓ -sum of L1-spaces |
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