On the basic sequence structure of variable exponent Lebesgue spaces

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 $P$.