LIPIcs.ITCS.2019.41.pdf
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The Paulsen Problem Made Simple
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10th Innovations in Theoretical Computer Science Conference (ITCS 2019)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Innovations in Theoretical Computer Science Conference (ITCS) - License:
Creative Commons Attribution 3.0 Unported license
- Publication Date: 2019-01-08
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Linus Hamilton and Ankur Moitra. The Paulsen Problem Made Simple. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 41:1-41:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
https://doi.org/10.4230/LIPIcs.ITCS.2019.41
https://doi.org/10.4230/LIPIcs.ITCS.2019.41
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).
Subject Classification
ACM Subject Classification
- Theory of computation → Design and analysis of algorithms
Keywords
- radial isotropic position
- operator scaling
- Paulsen problem
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