Let (Ω,Σ,μ) be a complete finite measure space and X a Banach space. 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 if and only if X does.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-6,
author = {Juan Carlos Ferrando},
title = {Copies of $l\_{[?]}$ in the space of Pettis integrable functions with integrals of finite variation},
journal = {Studia Mathematica},
volume = {209},
year = {2012},
pages = {93-98},
zbl = {1257.46020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-6}
}
Juan Carlos Ferrando. Copies of $ℓ_{∞}$ in the space of Pettis integrable functions with integrals of finite variation. Studia Mathematica, Tome 209 (2012) pp. 93-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm210-1-6/