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A note on Schroeder-Bernstein property and primary property of Orlicz function spaces. (English) Zbl 0937.46010
Let $$X$$ be a reflexive Orlicz function space. If $$Y$$ is a complemented subspace of $$X$$ which, in turn, contains a complemented subspace isomorphic to $$X$$, then $$Y$$ itself is isomorphic to $$X$$. Also, the Banach space $$X$$ is primary; that is, for every decomposition of $$X$$ into a direct sum of two subspaces, at least one of the factors is isomorphic to $$X$$ itself.

##### MSC:
 46B20 Geometry and structure of normed linear spaces 46A25 Reflexivity and semi-reflexivity
##### Keywords:
Orlicz function space; complemented subspace; reflexivity
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