The multiplicative property characterizes $\ell_p$ and $L_p$ norms

Details The multiplicative property characterizes $\ell_p$ and $L_p$ norms The multiplicative property characterizes $\ell_p$ and $L_p$ norms

2011-02-13

arxiv.org/abs/1102.2618v1

Mathematics

Functional Analysis

8 pages, 1 figure

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The multiplicative property characterizes $\ell_p$ and $L_p$ norms does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The multiplicative property characterizes $\ell_p$ and $L_p$ norms, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The multiplicative property characterizes $\ell_p$ and $L_p$ norms will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-521