Abstract
The statements in the title are explained and proved, as a little exercise in elementary normed vector space theory at the level of Chap. 5 of Dieudonné’s Foundations of Mathematical Analysis. A connection to recent moment bounds for submartingales is sketched.
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Mattner, L. Sums of norm spheres are norm shells and lower triangle inequalities are sharp . Math. Semesterber. 57, 11–16 (2010). https://doi.org/10.1007/s00591-009-0063-9
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DOI: https://doi.org/10.1007/s00591-009-0063-9