Acta Mathematica Hungarica

, Volume 135, Issue 1–2, pp 24–30 | Cite as

Copies of c0 in the space of Pettis integrable functions with integrals of finite variation

Article

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 c0 if and only if X does.

Keywords

Pettis integrable function countably additive vector measure of bounded variation copy of c0 

2000 Mathematics Subject Classification

28B05 46B03 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  1. 1.Centro de Investigación Operativa, Edificio TorretamaritAvda de la Universidad, Universidad Miguel HernándezElche (Alicante)Spain

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