Rademacher functions in BMO
The Rademacher sums are investigated in the BMO space on (0;1). They span an uncomplemented subspace, in contrast to the dyadic BMOd space on (0;1), where they span a complemented subspace isomorphic to l2. Moreover, structural properties of infinite-dimensional closed subspaces of the span of the Rademacher functions in BMO are studied and an analog of the Kadec-Peczy«ski type alternative with l2 and c0 spaces is proved.