Noncommutative Valdivia compacta
Functional Analysis
2014-01-30 v1
Abstract
We prove some generalizations of results concerning Valdivia compact spaces (equivalently spaces with a commutative retractional skeleton) to the spaces with a retractional skeleton (not necessarily commutative). Namely, we show that the dual unit ball of a Banach space is Corson provided the dual unit ball of every equivalent norm has a retractional skeleton. Another result to be mentioned is the following. Having a compact space K, we show that K is Corson if and only if every continuous image of K has a retractional skeleton.
Cite
@article{arxiv.1301.5799,
title = {Noncommutative Valdivia compacta},
author = {Marek Cuth},
journal= {arXiv preprint arXiv:1301.5799},
year = {2014}
}