Abstract:Let $E^{\varphi }(\mu )$ be the subspace of finite elements of an Orlicz space endowed with the Luxemburg norm. The main theorem says that a compact linear operator $T:E^{\varphi }(\mu )\rightarrow C(\Omega )$ is extreme if and only if $T^{*}\omega \in Ext B((E^{\varphi }(\mu ))^{*})$ on a dense subset of $\Omega $, where $\Omega $ is a compact Hausdorff topological space and $\langle T^{*}\omega ,x\rangle =(T x)(\omega )$. This is done via the description of the extreme points of the space of continuous functions $C(\Omega ,L^{\varphi }(\mu ))$, $L^{\varphi }(\mu )$ being an Orlicz space equipped with the Orlicz norm (conjugate to the Luxemburg one). There is also given a theorem on closedness of the set of extreme points of the unit ball with respect to the Orlicz norm.
Keywords: extreme points, vector valued continuous functions, compact linear operators, Orlicz spaces
AMS Subject Classification: 46E30, 46B20