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 | |
| Added by: | [mc] |
| Total mark: | 0 |
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