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Note on Kadets Klee property and Asplund spaces

Authors: Petr Hájek and Jarno Talponen
Journal: Proc. Amer. Math. Soc. 142 (2014), 3933-3939
MSC (2010): Primary 46B03, 46B20
Published electronically: July 24, 2014
MathSciNet review: 3251733
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Abstract: A typical result in this note is that if $ X$ is a Banach space which is a weak Asplund space and has the $ \omega ^*$-$ \omega $-Kadets Klee property, then $ X$ is already an Asplund space.

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Petr Hájek
Affiliation: Mathematical Institute, Czech Academy of Science, Žitná 25, 115 67 Praha 1, Czech Republic – and – Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Zikova 4, 160 00, Prague, Czech Republic

Jarno Talponen
Affiliation: Aalto University, Institute of Mathematics, P.O. Box 11100, FI-00076 Aalto, Finland
Address at time of publication: University of Eastern Finland, Institute of Mathematics, Box 111, FI-80101 Joensuu, Finland

Keywords: Asplund spaces, weak-star Kadets Klee property, weak-star-to-weak Kadets Klee property, Grothendieck spaces, renormings, duality mapping, WLD, weakly Lindel\"of determined, SCP, separable complementation property, coseparable subspaces
Received by editor(s): August 21, 2012
Received by editor(s) in revised form: December 11, 2012, and December 19, 2012
Published electronically: July 24, 2014
Additional Notes: The first author was financially supported by grant GACR 201/11/0345 and was supported in part by Institutional Research Plan AV0Z10190503 and GAČR P201/11/0345.
This paper was prepared as the second author enjoyed the warm hospitality of the Czech Academy of Sciences in autumn 2011. The visit and research were supported in part by the Väisälä Foundation.
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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