Norming subspaces of Banach spaces

Vladimir P. Fonf; Sebastian Lajara; Stanimir Troyanski; Clemente Zanco

Norming subspaces of Banach spaces

Functional Analysis 2018-04-27 v1

Authors: Vladimir P. Fonf , Sebastian Lajara , Stanimir Troyanski , Clemente Zanco

Abstract

We show that, if $X$ is a closed subspace of a Banach space $E$ and $Z$ is a closed subspace of $E^*$ such that $Z$ is norming for $X$ and $X$ is total over $Z$ (as well as $X$ is norming for $Z$ and $Z$ is total over $X$ ), then $X$ and the pre-annihilator of $Z$ are complemented in $E$ whenever $Z$ is $w^*$ -closed or $X$ is reflexive.

Keywords

banach spaces

Cite

@article{arxiv.1804.09968,
  title  = {Norming subspaces of Banach spaces},
  author = {Vladimir P. Fonf and Sebastian Lajara and Stanimir Troyanski and Clemente Zanco},
  journal= {arXiv preprint arXiv:1804.09968},
  year   = {2018}
}

Related papers

View all related →