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 {rj1 (t)× rj2 (t)…rjd (t)}(j1,j2,…,jd)εA in a symmetric space X implies its equivalence in X to the canonical basis in l2. In the special case of Orlicz spaces LM, unconditionality of this system is also shown to be equivalent to the fact that a certain exponential Orlicz space embeds into LM.