English

Complemented copies of $\ell_1$ in spaces of vector valued measures and applications

Functional Analysis 2016-09-06 v1

Abstract

Let XX be a Banach space and (Ω,Σ)(\Omega,\Sigma) be a measure space. We provide a characterization of sequences in the space of XX-valued countably additive measures on Ω,Σ)\Omega,\Sigma) of bounded variation that generate complemented copies of 1\ell_1. As application, we prove that if a dual Banach space EE^* has Pe\l czy\'nski's property (V*) then so does the space of EE^*-valued countably additive measures with bounded variation. Another application, we show that for a Banach space XX, the space (X)\ell_\infty(X) contains a complemented copy of 1\ell_1 if and only if XX contains all 1n\ell_1^n 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}
}