Sums of norm spheres are norm shells and lower triangle inequalities are sharp
Classical Analysis and ODEs
2009-09-01 v3
Abstract
The statements in the title are explained and proved, as a little exercise in elementary normed vector space theory at the level of Chapter 5 of Dieudonn\'e's "Foundations of Mathematical Analysis". A connection to recent moment bounds for submartingales is sketched.
Keywords
Cite
@article{arxiv.0805.0314,
title = {Sums of norm spheres are norm shells and lower triangle inequalities are sharp},
author = {Lutz Mattner},
journal= {arXiv preprint arXiv:0805.0314},
year = {2009}
}
Comments
6 pages. New additional introduction explaining connection to recent moment bounds for submartingales. This version accepted for publication in "Mathematische Semesterberichte"