This is an announcement for the paper "Modulus of supporting convexity and supporting smoothness" by Grigory Ivanov.

Abstract: We introduce the moduli of the supporting convexity and the supporting smoothness of the Banach space which characterize the deviation of the unit sphere from an arbitrary supporting hyperplane. We show that the modulus of supporting smoothness, the Banas modulus, and the modulus of smoothness are equivalent at zero, respectively the modulus of supporting convexity is equivalent at zero to the modulus of convexity. We prove a Day-Nordlander type result for these moduli.

Archive classification: math.FA

Submitted from: grigory.ivanov@phystech.edu

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1503.08912

or

http://arXiv.org/abs/1503.08912