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This article is cited in 2 scientific papers (total in 2 papers)
Brief communications
Multipliers on the Set of Rademacher Series in Symmetric Spaces
G. P. Curberaa, V. A. Rodinb a University of Seville
b Voronezh Institute of Russian Ministry of Internal Affairs
Abstract:
Let $E$ be a symmetric space on $[0,1]$. Let $\Lambda(\mathcal{R},E)$ be the space of measurable functions $f$ such that $fg\in E$ for every almost everywhere convergent series $g=\sum b_nr_n\in E$, where $(r_n)$ are the Rademacher functions. In [G. P. Curbera, Proc. Edinb. Math. Soc., 40, No. 1, 119–126 (1997)] it was shown that, for a broad class of spaces $E$, the space $\Lambda(\mathcal{R},E)$ is not order isomorphic to a symmetric space, and we study the conditions under which such an isomorphism exists. We give conditions on $E$ for $\Lambda(\mathcal{R},E)$ to be order isomorphic to $L_\infty$. This includes some classes of Lorentz and Marcinkiewicz spaces. We also study the conditions under which $\Lambda(\mathcal{R},E)$ is order isomorphic to a symmetric space that differs from $L_\infty$. The answer is positive for the Orlicz spaces $E=L_{\Phi_q}$ with $\Phi_q(t)=\exp|t|^q-1$ and $0<q<2$.
Keywords:
Rademacher series in symmetric spaces, Orlicz and Marcinkiewicz spaces, multiplier for Rademacher series.
Received: 09.11.2000
Citation:
G. P. Curbera, V. A. Rodin, “Multipliers on the Set of Rademacher Series in Symmetric Spaces”, Funktsional. Anal. i Prilozhen., 36:3 (2002), 87–90; Funct. Anal. Appl., 36:3 (2002), 244–246
Linking options:
https://www.mathnet.ru/eng/faa212https://doi.org/10.4213/faa212 https://www.mathnet.ru/eng/faa/v36/i3/p87
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