English

The Gau-Wang-Wu conjecture on partial isometries holds in the 5-by-5 case

Functional Analysis 2021-08-17 v1

Abstract

Gau, Wang and Wu in their LAMA'2016 paper conjectured (and proved for n4n\leq 4) that an nn-by-nn partial isometry cannot have a circular numerical range with a non-zero center. We prove that this statement holds also for n=5n=5.

Keywords

Cite

@article{arxiv.2108.07024,
  title  = {The Gau-Wang-Wu conjecture on partial isometries holds in the 5-by-5 case},
  author = {Ilya M. Spitkovsky and Ibrahim Suleiman and Elias Wegert},
  journal= {arXiv preprint arXiv:2108.07024},
  year   = {2021}
}

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10 pages