Asymptotic Smoothness, Convex Envelopes and Polynomial Norms
Functional Analysis
2016-04-21 v2
Abstract
We introduce a suitable notion of asymptotic smoothness on infinite dimensional Banach spaces, and we prove that, under some structural restrictions on the space, the convex envelope of an asymptotically smooth function is asymptotically smooth. Furthermore, we study convexity and smoothness properties of polynomial norms, and we obtain that a polynomial norm of degree N has modulus of convexity of power type N.
Keywords
Cite
@article{arxiv.1512.05407,
title = {Asymptotic Smoothness, Convex Envelopes and Polynomial Norms},
author = {Jesús A. Jaramillo and Raquel Gonzalo and Diego Yáñez},
journal= {arXiv preprint arXiv:1512.05407},
year = {2016}
}