On unconditionality of fractional Rademacher chaos in symmetric spaces

Abstract

We study density estimates of an index set A under which the unconditionality (or even the weaker property of random unconditional divergence) of the corresponding Rademacher fractional chaos {r(j1) (t) x r(j2) (t) center dot center dot center dot r(jd) (t)}( j(1),j(2),...,j(d)) is an element of A in a symmetric space X implies its equivalence in X to the canonical basis in l(2). In the special case of Orlicz spaces L-M, unconditionality of this system is also shown to be equivalent to the fact that a certain exponential Orlicz space embeds into L-M.