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We find conditions on a function space L that ensure that it behaves as an Lₚ-space in the sense that any unconditional basis of a complemented subspace of L either is equivalent to the unit vector system of ₂ or has a subbasis equivalent to a disjointly supported basic sequence. This dichotomy allows us to classify the symmetric basic sequences of L. Several applications to Orlicz function spaces are provided.
Ansorena et al. (Fri,) studied this question.