Rademacher multiplicator spaces equal to 𝐿^{∞}

Astashkin, Serguei; Curbera, Guillermo

doi:10.1090/S0002-9939-08-09542-7

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.

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