On Moduli of Convexity in Banach Spaces

Author: Bárcenas Diómedes   Gurariy Vladimir   Sánchez Luisa   Ullán Antonio  

Publisher: Taylor & Francis Ltd

ISSN: 1607-3606

Source: Quaestiones Mathematicae, Vol.27, Iss.2, 2004-06, pp. : 137-145

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Abstract

We provide an example to show that the moduli of convexity δE and βE are different. Our example allows us to prove that 2 is the best possible constant in the inequality δE ≤ β E ≤ 2 δ E and that βE does not need to be a convex function.