On the basic sequence structure of variable exponent Lebesgue spaces

Abstract

We study the subsymmetric basic sequence structure of variable exponent Lebesgue spaces $L_P$ built from index functions $P:\hat{I}\text{c◯}\to (0,\infty ]$ on $\ddot{I}ƒ$-finite measure spaces $(\hat{I}\text{c◯},\hat{I}\pounds ,\hat{I}¼)$. 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 $P$.

27 pages