The Paulsen Problem Made Simple
Name
LIPIcs-ITCS-2019-41.pdf
Description
Published version
Size
373.24 KB
Format
Unknown
Checksum (MD5)
39b30b1b34e96dbff2ed1cfac3579f09
Author(s)
Hamilton, Linus
Moitra, Ankur
Date Issued
2019
Citation
Hamilton, Linus and Moitra, Ankur. 2019. "The Paulsen Problem Made Simple."
Version
Final published version
Abstract
© Linus Hamilton and Ankur Moitra. 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 -nearly equal norm Parseval frame in d dimensions is within squared distance O(?d13/2) 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(ϵd2).
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution 4.0 International license
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.4230/LIPIcs.ITCS.2019.41
