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On moduli of convexity in Banach spaces


Let be a normed linear space, an element of norm one, and and the local modulus of convexity of. We denote by the greatest such that for each closed linear subspace of the quotient mapping maps the open-neighbourhood of in onto a set containing the open-neighbourhood of in. It is known that. We prove that there is no universal constant such that, however, such a constant exists within the class of Hilbert spaces. If is a Hilbert space with, then.

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Correspondence to Jiří Reif.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Reif, J. On moduli of convexity in Banach spaces. J Inequal Appl 2005, 695306 (2005).

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