On $\ell_\infty$-Grothendieck subspaces

Manuel González; Fernando León-Saavedra; María del Pilar Romero de la Rosa

On $\ell_\infty$-Grothendieck subspaces

Functional Analysis 2020-12-22 v1

Authors: Manuel González , Fernando León-Saavedra , María del Pilar Romero de la Rosa

Abstract

A closed subspace $S$ of $\ell_\infty$ is said to be a \emph{ $\ell_\infty$ -Grothendieck subspace} if $c_0\subset S$ (hence $\ell_\infty\subset S^{**}$ ) and every $\sigma(S^*,S)$ -convergent sequence in $S^*$ is $\sigma(S^*,\ell_\infty)$ -convergent. Here we give examples of closed subspaces of $\ell_\infty$ containing $c_0$ which are or fail to be $\ell_\infty$ -Grothendieck.

Cite

@article{arxiv.2012.10676,
  title  = {On $\ell_\infty$-Grothendieck subspaces},
  author = {Manuel González and Fernando León-Saavedra and María del Pilar Romero de la Rosa},
  journal= {arXiv preprint arXiv:2012.10676},
  year   = {2020}
}

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