Displaying similar documents to “The James constant of normalized norms on ℝ 2 .”

A universal modulus for normed spaces

Carlos Benítez, Krzysztof Przesławski, David Yost (1998)

Studia Mathematica

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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.

An inequality between the James and James type constants in Banach spaces

Fenghui Wang, Changsen Yang (2010)

Studia Mathematica

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We consider the James and Schäffer type constants recently introduced by Takahashi. We prove an equality between James (resp. Schäffer) type constants and the modulus of convexity (resp. smoothness). By using these equalities, we obtain some estimates for the new constants in terms of the James constant. As a result, we improve an inequality between the Zbăganu and James constants.