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

Juan Carlos Ferrando. "Copies of $ℓ_{∞}$ in the space of Pettis integrable functions with integrals of finite variation." Studia Mathematica 210.1 (2012): 93-98. <http://eudml.org/doc/285766>.

@article{JuanCarlosFerrando2012,
abstract = {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 $ℓ_\{∞\}$ if and only if X does.},
author = {Juan Carlos Ferrando},
journal = {Studia Mathematica},
keywords = {Pettis integrable function; countably additive vector measure of bounded variation; copy of },
language = {eng},
number = {1},
pages = {93-98},
title = {Copies of $ℓ_\{∞\}$ in the space of Pettis integrable functions with integrals of finite variation},
url = {http://eudml.org/doc/285766},
volume = {210},
year = {2012},
}

TY - JOUR
AU - Juan Carlos Ferrando
TI - Copies of $ℓ_{∞}$ in the space of Pettis integrable functions with integrals of finite variation
JO - Studia Mathematica
PY - 2012
VL - 210
IS - 1
SP - 93
EP - 98
AB - 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 $ℓ_{∞}$ if and only if X does.
LA - eng
KW - Pettis integrable function; countably additive vector measure of bounded variation; copy of
UR - http://eudml.org/doc/285766
ER -