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ArticleOriginal scientific text

Title

A universal modulus for normed spaces

Authors 1, 2, 3

Affiliations

  1. Departamento de Matemáticas, Universidad de Extremadura, 06071 Badajoz, Spain
  2. Institute of Mathematics, Technical University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland
  3. Bâtiment 101-Mathématiques, Université de Lyon 1, Boulevard du 11 Novembre 1918, 69622 Villeurbanne Cedex, France

Abstract

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.

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Studia Mathematica
1998/127/1
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Pages:
21-46
Main language of publication
English
Received
1996-07-01
Accepted
1997-06-10
Published
1998
Exact and natural sciences