Asymptotic geometry of Banach spaces and uniform quotient maps
Functional Analysis
2012-09-05 v1 Metric Geometry
Abstract
Recently, Lima and Randrianarivony pointed out the role of the property of Rolewicz in nonlinear quotient problems, and answered a ten-year-old question of Bates, Johnson, Lindenstrauss, Preiss and Schechtman. In the present paper, we prove that the modulus of asymptotic uniform smoothness of the range space of a uniform quotient map can be compared with the modulus of of the domain space. We also provide conditions under which this comparison can be improved.
Keywords
Cite
@article{arxiv.1209.0501,
title = {Asymptotic geometry of Banach spaces and uniform quotient maps},
author = {S. J. Dilworth and Denka Kutzarova and G. Lancien and N. L. Randrianarivony},
journal= {arXiv preprint arXiv:1209.0501},
year = {2012}
}