[Banach] Abstract of a paper by Guillaume Aubrun and Ion Nechita

This is an announcement for the paper "The multiplicative property characterizes $\ell_p$ and $L_p$ norms" by Guillaume Aubrun and Ion Nechita.

Abstract: We show that $\ell_p$ norms are characterized as the unique norms which are both invariant under coordinate permutation and multiplicative with respect to tensor products. Similarly, the $L_p$ norms are the unique rearrangement-invariant norms on a probability space such that $|X Y|=|X|\cdot|Y|$ for every pair $X,Y$ of independent random variables. Our proof relies on Cram'er's large deviation theorem.

Archive classification: math.FA

Remarks: 8 pages, 1 figure

Submitted from: inechita@uottawa.ca

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1102.2618

or

http://arXiv.org/abs/1102.2618