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PreprintCC BY 4.0arXiv

Applications of the Projection Characterization and Symmetry Bootstrap for Operators that are Nearby Commuting Operators

  • David Herrera
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Abstract

This paper applies the Projection Characterization and the Symmetry Bootstrap for two operators $A, B$ (with A unitary or self-adjoint) nearby commuting operators $A', B'$ (with A' unitary or self-adjoint) from arXiv:2412.20795 to problems related to structured almost commuting unitaries, self-adjoint operators that almost anti-commute, and unitaries that almost commute up to a rational phase. We prove several new stability theorems for these types of relations for matrices. We also provide estimates for how close the constructed operators are for several known stability theorems that did not previously have asymptotic estimates.

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Cite

BibTeXRIS
BibTeX
@misc{herrera2026applications,
  title = {{Applications of the Projection Characterization and Symmetry Bootstrap for Operators that are Nearby Commuting Operators}},
  author = {David Herrera},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15057},
  eprint = {2609.15057},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15057},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Applications of the Projection Characterization and Symmetry Bootstrap for Operators that are Nearby Commuting Operators
AU  - David Herrera
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15057
UR  - https://arxiv.org/abs/2609.15057
AB  - This paper applies the Projection Characterization and the Symmetry Bootstrap for two operators $A, B$ (with A unitary or self-adjoint) nearby commuting operators $A', B'$ (with A' unitary or self-adjoint) from arXiv:2412.20795 to problems related to structured almost commuting unitaries, self-adjoint operators that almost anti-commute, and unitaries that almost commute up to a rational phase. We prove several new stability theorems for these types of relations for matrices. We also provide estimates for how close the constructed operators are for several known stability theorems that did not previously have asymptotic estimates.
ER  -