This is an announcement for the paper "Using boundaries to find smooth norms" by Victor Bible.

Abstract: The aim of this paper is to present a tool used to find Banach spaces which have a C^{\infty} smooth equivalent norm. 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.

Archive classification: math.FA

Mathematics Subject Classification: 46B03

Remarks: 11 pages

Submitted from: victor.bible@ucdconnect.ie

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1311.1408

or

http://arXiv.org/abs/1311.1408