A universal modulus for normed spaces

Tom 127 / 1998

Carlos Benítez, Krzysztof Przesławski, David Yost Studia Mathematica 127 (1998), 21-46 DOI: 10.4064/sm-127-1-21-46


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.


  • Carlos Benítez
  • Krzysztof Przesławski
  • David Yost

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek