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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the topology of pointwise convergence on the boundaries of $ L_1$-preduals


Authors: Warren B. Moors and Jirí Spurny
Journal: Proc. Amer. Math. Soc. 137 (2009), 1421-1429
MSC (2000): Primary 46A50; Secondary 46B20
Published electronically: October 29, 2008
MathSciNet review: 2465668
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Abstract: In this paper we prove a theorem more general than the following:

``If $ (X,\Vert\cdot\Vert)$ is an $ L_1$-predual, $ B$ is any boundary of $ X$ and $ \{x_n:n \in \N\}$ is any subset of $ X$, then the closure of $ \{x_n:n \in \N\}$ with respect to the topology of pointwise convergence on $ B$ is separable with respect to the topology generated by the norm, whenever $ {\rm Ext}(B_{X^*})$ is weak$ ^*$ Lindelöf.'' Several applications of this result are also presented.


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Additional Information

Warren B. Moors
Affiliation: Department of Mathematics, The University of Auckland, Private Bag 92019, Auckland, New Zealand
Email: moors@math.auckland.ac.nz

Jirí Spurny
Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: spurny@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09708-6
PII: S 0002-9939(08)09708-6
Keywords: Compact convex, extreme points, boundary, $L_1$-predual.
Received by editor(s): May 22, 2008
Published electronically: October 29, 2008
Additional Notes: The second author was supported by the research project MSM 0021620839 financed by MSMT and by the grant GAČR 201/07/0388.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2008 American Mathematical Society