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

 

A full description of extreme points in $ C(\Omega,L\sp \phi(\mu))$


Author: Marek Wisła
Journal: Proc. Amer. Math. Soc. 113 (1991), 193-200
MSC: Primary 46E40; Secondary 46E30
MathSciNet review: 1072351
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Abstract: Let $ {L^\varphi }(\mu )$ be an Orlicz space endowed with the Luxemburg norm. The main result of this paper reads as follows: $ f$ is an extreme point of the unit ball of the space of continuous functions from a compact Hausdorff space $ \Omega $ into $ {L^\varphi }(\mu )$ with the supremum norm if and only if the inverse image of the set of all extreme points of the unit ball of $ {L^\varphi }(\mu )$ under $ f$ is dense in $ \Omega $.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1072351-6
PII: S 0002-9939(1991)1072351-6
Keywords: Extreme points, vector valued functions, spaces of continuous functions, Orlicz spaces
Article copyright: © Copyright 1991 American Mathematical Society