Rademacher functions in BMO
Volume 205 / 2011
Studia Mathematica 205 (2011), 83-100 MSC: 46E30, 46B20, 46B42. DOI: 10.4064/sm205-1-6
The Rademacher sums are investigated in the $BMO$ space on $[0, 1]$. They span an uncomplemented subspace, in contrast to the dyadic $BMO_d$ space on $[0, 1]$, where they span a complemented subspace isomorphic to $l_2$. 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–Pełczyński type alternative with $l_2$ and $c_0$ spaces is proved.