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Rademacher multiplicator spaces equal to $ L^\infty$

Authors: Serguei V. Astashkin and Guillermo P. Curbera
Journal: Proc. Amer. Math. Soc. 136 (2008), 3493-3501
MSC (2000): Primary 46E35, 46E30; Secondary 47G10
Published electronically: May 29, 2008
MathSciNet review: 2415033
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Abstract: Let $ X$ be a rearrangement invariant function space on [0,1]. We consider the Rademacher multiplicator space $ \Lambda(\mathcal{R},X)$ of measurable functions $ x$ such that $ x\cdot h\in X$ for every a.e. converging series $ h=\sum a_nr_n\in X$, where $ (r_n)$ are the Rademacher functions. We characterize the situation when $ \Lambda(\mathcal{R},X)= L^\infty$. We also discuss the behaviour of partial sums and tails of Rademacher series in function spaces.

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Additional Information

Serguei V. Astashkin
Affiliation: Department of Mathematics and Mechanics, Samara State University, ul. Akad. Pavlova 1, 443011 Samara, Russia

Guillermo P. Curbera
Affiliation: Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain

Keywords: Rademacher functions, rearrangement invariant space
Received by editor(s): May 3, 2007
Published electronically: May 29, 2008
Additional Notes: This work was partially supported by D.G.I. #BFM2006–13000–C03–01 (Spain).
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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