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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
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