Three and a half asymptotic properties
Functional Analysis
2018-05-09 v1
Abstract
We define and discuss transfinite asymptotic notions of smoothability, type, and equal norm type. We prove distinctness of these notions for a proper class of ordinals and that each class is an ideal. We also extend some results of Godefroy, Kalton, and Lancien to operators and ordinals greater than zero regarding the equivalence of equal norm asymptotic type and uniform renormings with power type smoothness. Finally, we discuss an extension of a non-linear result for quasi-reflexive, asymptotically -smoothable Banach spaces to quasi-reflexive Banach spaces with asymptotic equal norm type .
Keywords
Cite
@article{arxiv.1805.02747,
title = {Three and a half asymptotic properties},
author = {R. M. Causey},
journal= {arXiv preprint arXiv:1805.02747},
year = {2018}
}