On the basic sequence structure of variable exponent Lebesgue spaces

José L. Ansorena; Glenier Bello

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arXiv · 2512.19538

On the basic sequence structure of variable exponent Lebesgue spaces

José L. Ansorena·Glenier Bello

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Abstract

We study the subsymmetric basic sequence structure of variable exponent Lebesgue spaces $L_{P}$ built from index functions $P\colon\Omega\to(0,\infty]$ on $\sigma$-finite measure spaces $(\Omega,\Sigma,\mu)$. Specifically, we prove that if $P$ is bounded away from infinity, then any complemented subsymmetric basic sequence of $L_{P}$ is equivalent to the canonical basis of $\ell_r$ for some $r\ge 1$ in the essential range of $P$.

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BibTeX RIS

José L. Ansorena, Glenier Bello. 2025-12-22. On the basic sequence structure of variable exponent Lebesgue spaces. https://arxiv.org/abs/2512.19538

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