Copies of $\ell _{\infty }$ in the space of Pettis integrable functions with integrals of finite variation
Volume 210 / 2012
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.
