Norming subspaces of Banach spaces

Fonf, V.; Lajara, S.; Troyanski, S.; Zanco, C.

doi:10.1090/proc/14442

Norming subspaces of Banach spaces
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by V. P. Fonf, S. Lajara, S. Troyanski and C. Zanco PDF

Proc. Amer. Math. Soc. 147 (2019), 3039-3045 Request permission

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 preannihilator of $Z$ are complemented in $E$ whenever $Z$ is $w^*$-closed or $X$ is reflexive.

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