Journal of Inequalities and Applications
Volume 2005 (2005), Issue 4, Pages 423-433
On moduli of convexity in Banach spaces
Department of Mathematics, Faculty of Applied Sciences, University of West Bohemia, 306 14 Plzeň, Czech Republic
Received 15 September 2003
Copyright © 2005 Jiří Reif. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 .