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Rich families and projectional skeletons in Asplund WCG spaces
Type of publication: Article
Citation:
Publication status: Published
Journal: J. Math. Anal. Appl.
Volume: 448
Number: 2
Year: 2017
Pages: 1618–1632
URL: http://www.sciencedirect.com/s...
DOI: 10.1016/j.jmaa.2016.11.081
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.
Preprint year: 2016
Keywords:
Authors Cúth, Marek
Fabian, Marian
Added by: [mc]
Total mark: 0
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