Geodesic
Copies of $\ell _{\infty }$ in the space of Pettis integrable functions with integrals of finite variation
Juan Carlos Ferrando 1
1 Centro de Investigación Operativa Universidad Miguel Hernández Edificio Torretamarit, Avda de la Universidad s/n E-03202 Elche (Alicante), Spain
Studia Mathematica, Tome 210 (2012) no. 1, pp. 93-98 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $ ( \varOmega ,\varSigma ,\mu ) $ be a complete finite measure space and $X$ a Banach space. We show that the space of all weakly $\mu $-measurable (classes of scalarly equivalent) $X$-valued Pettis integrable functions with integrals of finite variation, equipped with the variation norm, contains a copy of $\ell _{\infty }$ if and only if $X$ does.
DOI : 10.4064/sm210-1-6
Keywords: varomega varsigma complete finite measure space banach space space weakly measurable classes scalarly equivalent x valued pettis integrable functions integrals finite variation equipped variation norm contains copy ell infty only does

Juan Carlos Ferrando  1

1 Centro de Investigación Operativa Universidad Miguel Hernández Edificio Torretamarit, Avda de la Universidad s/n E-03202 Elche (Alicante), Spain 
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Juan Carlos Ferrando. Copies of $\ell _{\infty }$ in the space of Pettis integrable functions with integrals of finite variation. Studia Mathematica, Tome 210 (2012) no. 1, pp. 93-98. doi: 10.4064/sm210-1-6

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