[Banach] Abstract of a paper by Victor Bible

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