Norms as a function of p are linearly independent in finite dimensions
Functional Analysis
2019-09-16 v2
Abstract
We show that there are no non-trivial linear dependencies among p-norms of vectors in finite dimensions that hold for all p. The proof is by complex analytic continuation.
Cite
@article{arxiv.1102.5026,
title = {Norms as a function of p are linearly independent in finite dimensions},
author = {Greg Kuperberg},
journal= {arXiv preprint arXiv:1102.5026},
year = {2019}
}
Comments
1 page, 1 figure. Proof simplified thanks to the referee