This is an announcement for the paper "Khinchin inequality and Banach-Saks type properties in rearrangement-invariant spaces" by F. Sukochev and D. Zanin.
Abstract: \begin{abstract} {\it We study the class of all rearrangement-invariant (=r.i.) function spaces $E$ on $[0,1]$ such that there exists $0<q<1$ for which $ \Vert \sum_{_{k=1}}^n\xi_k\Vert _{E}\leq Cn^{q}$, where ${\xi_k}_{k\ge 1}\subset E$ is an arbitrary sequence of independent identically distributed symmetric random variables on $[0,1]$ and $C>0$ does not depend on $n$. We completely characterize all Lorentz spaces having this property and complement classical results of Rodin and Semenov for Orlicz spaces $exp(L_p)$, $p\ge 1$. We further apply our results to the study of Banach-Saks index sets in r.i. spaces. \end{abstract}
Archive classification: math.FA
Mathematics Subject Classification: 46E30 (46B09 46B20)
Citation: Studia Math. 191 (2009), no. 2, 101--122
The source file(s), sukochev_zanin_submitted.tex: 67832 bytes, is(are) stored in gzipped form as 1001.2432.gz with size 20kb. The corresponding postcript file has gzipped size 84kb.
Submitted from: zani0005@csem.flinders.edu.au
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