Grothendieck ordered Banach spaces with an interpolation property
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- by Ioannis A. Polyrakis and Foivos Xanthos PDF
- Proc. Amer. Math. Soc. 141 (2013), 1651-1661 Request permission
Abstract:
In this paper we prove that if $E$ is an ordered Banach space with the countable interpolation property, $E$ has an order unit and $E_+$ is closed and normal, then $E$ is a Grothendieck space; i.e. any weak-star convergent sequence of $E^*$ is weakly convergent. By the countable interpolation property we mean that for any $A,B\subseteq E$ countable, with $A\leq B$, we have $A\leq \{x\}\leq B$ for some $x\in E$.References
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Additional Information
- Ioannis A. Polyrakis
- Affiliation: Department of Mathematics, National Technical University of Athens, Zographou 157 80, Athens, Greece
- Email: ypoly@math.ntua.gr
- Foivos Xanthos
- Affiliation: Department of Mathematics, National Technical University of Athens, Zographou 157 80, Athens, Greece
- Email: fxanthos@math.ntua.gr
- Received by editor(s): February 14, 2011
- Received by editor(s) in revised form: September 5, 2011
- Published electronically: October 26, 2012
- Additional Notes: This research was supported by the HERAKLEITOS II project, which is co-funded by the European Social Fund and National Resources
- Communicated by: Thomas Schlumprecht
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 1651-1661
- MSC (2010): Primary 46B40, 46B42, 47B60
- DOI: https://doi.org/10.1090/S0002-9939-2012-11437-6
- MathSciNet review: 3020852