Modulus of supporting convexity and supporting smoothness
Functional Analysis
2015-11-17 v3
Abstract
We introduce the moduli of the supporting convexity and the supporting smoothness of a Banach space, which characterize the deviation of the unit sphere from an arbitrary supporting hyperplane. We show that the modulus of supporting smoothness, the Bana{\'s} modulus, and the modulus of smoothness are all equivalent at zero, the modulus of supporting convexity is equivalent at zero to the modulus of convexity. We prove a Day--Nordlander type result for these moduli.
Keywords
Cite
@article{arxiv.1503.08912,
title = {Modulus of supporting convexity and supporting smoothness},
author = {Grigory Ivanov},
journal= {arXiv preprint arXiv:1503.08912},
year = {2015}
}