Rademacher multiplicator spaces equal to $L^\infty$
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- by Serguei V. Astashkin and Guillermo P. Curbera PDF
- Proc. Amer. Math. Soc. 136 (2008), 3493-3501 Request permission
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.References
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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
- MR Author ID: 197703
- Email: astashkn@ssu.samara.ru
- Guillermo P. Curbera
- Affiliation: Facultad de Matemáticas, Universidad de Sevilla, Aptdo. 1160, Sevilla 41080, Spain
- MR Author ID: 312355
- Email: curbera@us.es
- 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
- © Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 3493-3501
- MSC (2000): Primary 46E35, 46E30; Secondary 47G10
- DOI: https://doi.org/10.1090/S0002-9939-08-09542-7
- MathSciNet review: 2415033