We define a handy new modulus for normed spaces. More precisely, given any normed space X, we define in a canonical way a function ξ:[0,1)→ ℝ which depends only on the two-dimensional subspaces of X. We show that this function is strictly increasing and convex, and that its behaviour is intimately connected with the geometry of X. In particular, ξ tells us whether or not X is uniformly smooth, uniformly convex, uniformly non-square or an inner product space.
@article{bwmeta1.element.bwnjournal-article-smv127i1p21bwm,
author = {Carlos Ben\'\i tez and Krzysztof Przes\l awski and David Yost},
title = {A universal modulus for normed spaces},
journal = {Studia Mathematica},
volume = {129},
year = {1998},
pages = {21-46},
zbl = {0909.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv127i1p21bwm}
}
Benítez, Carlos; Przesławski, Krzysztof; Yost, David. A universal modulus for normed spaces. Studia Mathematica, Tome 129 (1998) pp. 21-46. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv127i1p21bwm/
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