Using boundaries to find smooth norms
Volume 224 / 2014
Studia Mathematica 224 (2014), 169-181
MSC: 46B20, 46B03.
DOI: 10.4064/sm224-2-5
Abstract
The aim of this paper is to present a tool used to show that certain Banach spaces can be endowed with $C^k$ smooth equivalent norms. The hypothesis uses particular countable decompositions of certain subsets of $B_{X^*}$, namely boundaries. Of interest is that the main result unifies two quite well known results. In the final section, some new corollaries are given.
