Copies of c0 in the space of Pettis integrable functions with integrals of finite variation
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.
KeywordsPettis integrable function countably additive vector measure of bounded variation copy of c0
2000 Mathematics Subject Classification28B05 46B03
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