Complemented copies of $\ell_1$ in spaces of vector valued measures and applications
Functional Analysis
2016-09-06 v1
Abstract
Let be a Banach space and be a measure space. We provide a characterization of sequences in the space of -valued countably additive measures on of bounded variation that generate complemented copies of . As application, we prove that if a dual Banach space has Pe\l czy\'nski's property (V*) then so does the space of -valued countably additive measures with bounded variation. Another application, we show that for a Banach space , the space contains a complemented copy of if and only if contains all uniformly complemented.
Keywords
Cite
@article{arxiv.math/9511206,
title = {Complemented copies of $\ell_1$ in spaces of vector valued measures and applications},
author = {Narcisse Randrianantoanina},
journal= {arXiv preprint arXiv:math/9511206},
year = {2016}
}