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 : (0, ] on -finite m easure s paces (, , ).Specifically, we prove that if P is bounded away from infinity, t hen a ny complemented subsymmetric basic sequence of L P is equivalent to the canonical basis of r for some r 1 in the essential range of P .The paper that initiated the study of variable exponent Lebesgue spaces by basic sequence techniques was [11] (see also [10]).In it, the authors characterized in terms of the essential range of the variable exponent P the indices q [1, ) such that q isomorphically embeds