Geodesic
Rademacher functions in BMO
Sergey V. Astashkin 1   ; Mikhail Leibov 2   ; Lech Maligranda 3
1 Department of Mathematics and Mechanics Samara State University Akad. Pavlova 1 443011 Samara, Russia
2 Horton Point LLC 1180 Avenue of the Americas New York, NY 10036, U.S.A.
3 Department of Engineering Sciences and Mathematics Luleå University of Technology SE-971 87 Luleå, Sweden
Studia Mathematica, Tome 205 (2011) no. 1, pp. 83-100 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/sm205-1-6
Keywords: rademacher sums investigated bmo space span uncomplemented subspace contrast dyadic bmo space where span complemented subspace isomorphic moreover structural properties infinite dimensional closed subspaces span rademacher functions bmo studied analog kadec czy ski type alternative spaces proved

Sergey V. Astashkin  1   ; Mikhail Leibov  2   ; Lech Maligranda  3

1 Department of Mathematics and Mechanics Samara State University Akad. Pavlova 1 443011 Samara, Russia
2 Horton Point LLC 1180 Avenue of the Americas New York, NY 10036, U.S.A.
3 Department of Engineering Sciences and Mathematics Luleå University of Technology SE-971 87 Luleå, Sweden 
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Sergey V. Astashkin; Mikhail Leibov; Lech Maligranda. Rademacher functions in BMO. Studia Mathematica, Tome 205 (2011) no. 1, pp. 83-100. doi: 10.4064/sm205-1-6

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