Norming subspaces of Banach spaces
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 $Z$...
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| Format: | Artikel |
| Sprache: | eng |
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| Zusammenfassung: | 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. |
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| DOI: | 10.48550/arxiv.1804.09968 |