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arXiv · 2407.18660

Unconditional basic sequences in function spaces with applications to Orlicz spaces

José L. Ansorena·Glenier Bello
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Abstract

We find conditions on a function space $\bf{L}$ that ensure that it behaves as an $L_p$-space in the sense that any unconditional basis of a complemented subspace of $\bf{L}$ 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 $\bf{L}$. Several applications to Orlicz function spaces are provided.

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José L. Ansorena, Glenier Bello. 2024-07-26. Unconditional basic sequences in function spaces with applications to Orlicz spaces. https://doi.org/10.1007/s11117-024-01093-w

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