On the action of Lipschitz functions on vector-valued random sums
| dc.creator | van Neerven, Jan | |
| dc.creator | Veraar, Mark | |
| dc.date | 2005-04-22 | |
| dc.date.accessioned | 2026-07-07T05:19:20Z | |
| dc.date.available | 2026-07-07T05:19:20Z | |
| dc.description | Let $X$ be a Banach space and let $(ξ_j)_{j\ge 1}$ 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 $$ \Bigl(\E\Big\|\sum_{j=1}^n ξ_j f(x_j)\Big\|^2\Bigr)^{\frac12} \leq K \n f\n_{\rm Lip} \Bigl(\E\Big\|\sum_{j=1}^n ξ_j x_j\Big\|^2\Bigr)^{\frac12} $$ for all Lipschitz functions $f:X\to X$ satisfying $f(0)=0$ and all finite sequences $x_1,...,x_n$ in $X$. (2). $X$ is isomorphic to a Hilbert space. | |
| dc.description | 8 pages, to appear in Archiv der Mathematik (Basel) | |
| dc.identifier | https://arxiv.org/abs/math/0504452 | |
| dc.identifier | http://arxiv.org/abs/math/0504452 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/74987 | |
| dc.subject | Functional Analysis | |
| dc.subject | Probability | |
| dc.subject | 46C15, 46B09, 47B10 | |
| dc.title | On the action of Lipschitz functions on vector-valued random sums | |
| dc.type | text |