License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ITCS.2019.41
URN: urn:nbn:de:0030-drops-101347
URL: https://drops.dagstuhl.de/opus/volltexte/2018/10134/
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Hamilton, Linus ; Moitra, Ankur

The Paulsen Problem Made Simple

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LIPIcs-ITCS-2019-41.pdf (0.4 MB)

Abstract

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).

BibTeX - Entry

@InProceedings{hamilton_et_al:LIPIcs:2018:10134,
  author =	{Linus Hamilton and Ankur Moitra},
  title =	{{The Paulsen Problem Made Simple}},
  booktitle =	{10th Innovations in Theoretical Computer Science  Conference (ITCS 2019)},
  pages =	{41:1--41:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-095-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{124},
  editor =	{Avrim Blum},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/10134},
  URN =		{urn:nbn:de:0030-drops-101347},
  doi =		{10.4230/LIPIcs.ITCS.2019.41},
  annote =	{Keywords: radial isotropic position, operator scaling, Paulsen problem}
}

Keywords: radial isotropic position, operator scaling, Paulsen problem
Collection: 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Issue Date: 2018
Date of publication: 08.01.2019

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