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Copies of $\ell _{\infty }$ in the space of Pettis integrable functions with integrals of finite variation

Volume 210 / 2012

Juan Carlos Ferrando Studia Mathematica 210 (2012), 93-98 MSC: Primary 28B05; Secondary 46B03. DOI: 10.4064/sm210-1-6

Abstract

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.

Authors

  • Juan Carlos FerrandoCentro de Investigación Operativa
    Universidad Miguel Hernández
    Edificio Torretamarit, Avda de la Universidad s/n
    E-03202 Elche (Alicante), Spain
    e-mail

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