The ell_p norms enjoy the following property : || x \otimes y || = ||x|| . ||y||
We prove that this property characterizes ell_p norms among permutation-invariant norms on the space of finitely supported sequences.
The proof is based on the tensor power trick together with Cramér's large deviations theorem.
Here is a blog post at the n-Category Café where Tom Leinster reformulates our result in a slightly different form.
aubrun (arrobas) math. univ-lyon1. fr