The Rademacher sums are investigated in the BMO space on [0,1]. They span an uncomplemented subspace, in contrast to the dyadic 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-Pełczyński type alternative with l₂ and c₀ spaces is proved.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-6,
author = {Sergey V. Astashkin and Mikhail Leibov and Lech Maligranda},
title = {Rademacher functions in BMO},
journal = {Studia Mathematica},
volume = {204},
year = {2011},
pages = {83-100},
zbl = {1242.46034},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-6}
}
Sergey V. Astashkin; Mikhail Leibov; Lech Maligranda. Rademacher functions in BMO. Studia Mathematica, Tome 204 (2011) pp. 83-100. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm205-1-6/