Sums of norm spheres are norm shells and lower triangle inequalities are sharp
arXiv:0805.0314
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 Dieudonné's "Foundations of Mathematical Analysis". A connection to recent moment bounds for submartingales is sketched.
6 pages. New additional introduction explaining connection to recent moment bounds for submartingales. This version accepted for publication in "Mathematische Semesterberichte"