Unconditional basic sequences in function spaces with applications to Orlicz spaces

Abstract

We find conditions on a function space $\mathbf{L}$ that ensure that it behaves as an $L_p$-space in the sense that any unconditional basis of a complemented subspace of $\mathbf{L}$ either is equivalent to the unit vector system of ${\ell }_2$ or has a subbasis equivalent to a disjointly supported basic sequence. This dichotomy allows us to classify the symmetric basic sequences of $\mathbf{L}$. Several applications to Orlicz function spaces are provided.

36 pages