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Proceedings of the American Mathematical Society

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

 

 

Extreme points in $ C(K,L\sp \varphi(\mu))$


Author: Ryszard Grząślewicz
Journal: Proc. Amer. Math. Soc. 98 (1986), 611-614
MSC: Primary 46E40; Secondary 46A55, 46E30
DOI: https://doi.org/10.1090/S0002-9939-1986-0861761-3
MathSciNet review: 861761
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Abstract: Let $ {L^\phi }(\mu )$ denote an Orlicz space and let $ \phi $ satisfy the condition $ {\Delta _2}$. It is shown that the extreme points of the unit ball of the space of continuous functions from a compact Hausdorff space $ K$ into $ {L^\phi }(\mu )$ with supremum norm on $ C(K,{L^\phi }(\mu ))$ are precisely the functions with values in the set of extreme points of the unit ball of $ {\text{of }}{L^\phi }(\mu )$.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0861761-3
Keywords: Extreme point, space of vector-valued functions, Orlicz space
Article copyright: © Copyright 1986 American Mathematical Society