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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Extreme functionals on an upper semicontinuous function space


Authors: F. Cunningham and Nina M. Roy
Journal: Proc. Amer. Math. Soc. 42 (1974), 461-465
MSC: Primary 46E40
DOI: https://doi.org/10.1090/S0002-9939-1974-0328579-3
MathSciNet review: 0328579
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Abstract: A representation theorem is given for the extreme points of the dual ball of a vector valued function space X with upper semicontinuous norm defined on a compact Hausdorff space $ \Omega $. This generalizes the Arens-Kelley theorem which is the case $ X = C(\Omega )$.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0328579-3
Keywords: Extreme functional, uniform norm, function space, upper semicontinuous norm
Article copyright: © Copyright 1974 American Mathematical Society