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arXiv · 1603.09480

Rich families and projectional skeletons in Asplund WCG spaces

Marek Cuth·Marian Fabian
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Abstract

We show a way of constructing projectional skeletons using the concept of rich families in Banach spaces which admit a projectional generator. Our next result is that a Banach space $X$ is Asplund and weakly compactly generated if and only if there exists a commutative 1-projectional skeleton $(Q_\gamma:\ \gamma\in\Gamma)$ on $X$ such that $(Q_\gamma{}^*:\ \gamma\in\Gamma)$ is a commutative 1-projectional skeleton on $X^*$. We consider both, real and also complex, Banach spaces.

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BibTeXRIS

Marek Cuth, Marian Fabian. 2016-03-31. Rich families and projectional skeletons in Asplund WCG spaces. https://doi.org/10.1016/j.jmaa.2016.11.081

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