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  • 标题:The Paulsen Problem Made Simple
  • 本地全文:下载
  • 作者:Linus Hamilton ; Ankur Moitra
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2018
  • 卷号:124
  • 页码:1-6
  • DOI:10.4230/LIPIcs.ITCS.2019.41
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:The Paulsen problem is a basic problem in operator theory that was resolved in a recent tour-de-force work of Kwok, Lau, Lee and Ramachandran. In particular, they showed that every epsilon-nearly equal norm Parseval frame in d dimensions is within squared distance O(epsilon d^{13/2}) of an equal norm Parseval frame. We give a dramatically simpler proof based on the notion of radial isotropic position, and along the way show an improved bound of O(epsilon d^2).
  • 关键词:radial isotropic position; operator scaling; Paulsen problem
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