This is an announcement for the paper "On the action of Lipschitz functions on vector-valued random sums" by Jan van Neerven and Mark Veraar.

Abstract: Let $X$ be a Banach space and let $(\xi_j)_{j\ge 1}$ be an i.i.d. sequence of symmetric random variables with finite moments of all orders. We prove that the following assertions are equivalent: (1). There exists a constant $K$ such that $$ \Bigl(\E\Big|\sum_{j=1}^n \xi_j f(x_j)\Big|^2\Bigr)^{\frac12} \leq K \n f\n_{\rm Lip} \Bigl(\E\Big|\sum_{j=1}^n \xi_j x_j\Big|^2\Bigr)^{\frac12} $$ for all Lipschitz functions $f:X\to X$ satisfying $f(0)=0$ and all finite sequences $x_1,\dots,x_n$ in $X$. (2). $X$ is isomorphic to a Hilbert space.

Archive classification: Functional Analysis; Probability

Mathematics Subject Classification: 46C15, 46B09, 47B10

Remarks: 8 pages, to appear in Archiv der Mathematik (Basel)

The source file(s), lipschitzA.tex: 27762 bytes, is(are) stored in gzipped form as 0504452.gz with size 9kb. The corresponding postcript file has gzipped size 56kb.

Submitted from: m.c.veraar@math.tudelft.nl

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