Copies of c 0 in the space of Pettis integrable functions with integrals of finite variation

Author： Ferrando Juan  

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.135, Iss.1-2, 2012-04, pp. : 24-30

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Abstract

Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. If all X-valued Pettis integrals defined on (Ω,Σ,μ) have separable ranges we show that the space of all weakly μ-measurable (classes of scalarly equivalent) X-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of c 0 if and only if X does.

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