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

 

Isomorphisms of spaces of continuous affine functions on compact convex sets with Lindelöf boundaries


Authors: Pavel Ludvík and Jiří Spurný
Journal: Proc. Amer. Math. Soc. 139 (2011), 1099-1104
MSC (2010): Primary 46A55, 46E15, 54D20
Published electronically: August 10, 2010
MathSciNet review: 2745661
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Abstract: Let $ X,Y$ be compact convex sets such that every extreme point of $ X$ and $ Y$ is a weak peak point and both $ \operatorname{ext} X$ and $ \operatorname{ext} Y$ are Lindelöf spaces. We prove that if there exists an isomorphism $ T:\mathfrak{A}^c(X)\to \mathfrak{A}^c(Y)$ with $ \Vert T\Vert\cdot \Vert T^{-1}\Vert<2$, then $ \operatorname{ext} X$ is homeomorphic to $ \operatorname{ext} Y$. This generalizes results of C. H. Chu and H. B. Cohen.


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Additional Information

Pavel Ludvík
Affiliation: Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: ludvik@karlin.mff.cuni.cz

Jiří Spurný
Affiliation: Department of Mathematical Analysis, 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/S0002-9939-2010-10534-8
PII: S 0002-9939(2010)10534-8
Keywords: Compact convex set, extreme point, weak peak point, Lindelöf space, continuous affine function
Received by editor(s): January 7, 2010
Received by editor(s) in revised form: April 9, 2010
Published electronically: August 10, 2010
Additional Notes: The first author was supported by grant GAČR 401/09/H007.
The second author was supported in part by the grants GAAV IAA 100190901 and GAČR 201/07/0388, and in part by the Research Project MSM 0021620839 from the Czech Ministry of Education.
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.