Extreme points in 𝐶(𝐾,𝐿^{𝜑}(𝜇))

Grząślewicz, Ryszard

doi:10.1090/S0002-9939-1986-0861761-3

Extreme points in $C(K,L^ \varphi (\mu ))$
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by Ryszard Grząślewicz

Proc. Amer. Math. Soc. 98 (1986), 611-614

DOI: https://doi.org/10.1090/S0002-9939-1986-0861761-3

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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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