PreprintCC BY 4.0arXiv
Failure of Rational Dilation on the Tetrablock via Parrott Homomorphisms
Abstract
We determine the cotangent operator space structure at the origin of the tetrablock (denoted by πΌ). In particular we prove that COT0(πΌΜ ) =MIN(β12βββ) completely isometrically. This shows the existence of commuting tuple of operators having πΌΜ as a spectral set but not as a complete spectral set.
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BibTeX
@misc{mandal2026failure,
title = {{Failure of Rational Dilation on the Tetrablock via Parrott Homomorphisms}},
author = {Shubhankar Mandal and Samya Kumar Ray},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37698},
eprint = {2609.37698},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37698},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Failure of Rational Dilation on the Tetrablock via Parrott Homomorphisms
AU - Shubhankar Mandal
AU - Samya Kumar Ray
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37698
UR - https://arxiv.org/abs/2609.37698
AB - We determine the cotangent operator space structure at the origin of the tetrablock (denoted by πΌ). In particular we prove that COT_0(πΌΜ
) =MIN(β_1^2β_ββ) completely isometrically. This shows the existence of commuting tuple of operators having πΌΜ
as a spectral set but not as a complete spectral set.
ER -