On the topology of pointwise convergence on the boundaries of $L_1$-preduals
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- by Warren B. Moors and Jiří Spurný PDF
- Proc. Amer. Math. Soc. 137 (2009), 1421-1429 Request permission
Abstract:
In this paper we prove a theorem more general than the following: “If $(X,\|\cdot \|)$ is an $L_1$-predual, $B$ is any boundary of $X$ and $\{x_n:n \in \mathbb {N} \}$ is any subset of $X$, then the closure of $\{x_n:n \in \mathbb {N} \}$ with respect to the topology of pointwise convergence on $B$ is separable with respect to the topology generated by the norm, whenever $\textrm {Ext}(B_{X^*})$ is weak$^*$ Lindelöf.” Several applications of this result are also presented.References
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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
- Jiří Spurný
- Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
- Email: spurny@karlin.mff.cuni.cz
- 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 GA ČR 201/07/0388.
- Communicated by: Nigel J. Kalton
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 1421-1429
- MSC (2000): Primary 46A50; Secondary 46B20
- DOI: https://doi.org/10.1090/S0002-9939-08-09708-6
- MathSciNet review: 2465668