发表机构
The Institute of Mathematical Sciences; Homi Bhabha National Institute（数学科学研究所; 霍米·巴巴国立研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过Parrott同态证明了四块体上存在以$\overline{\mathbb E}$为谱集但不为完全谱集的交换算子元组，从而表明有理膨胀在该域上失败。
AI 中文摘要
我们确定了四块体（记为$\mathbb E$）在原点的余切算子空间结构。特别地，我们证明了$\operatorname{COT}_0(\overline{\mathbb E}) =\operatorname{MIN}(\ell_1^2\oplus_\infty\mathbb C)$完全等距同构。这表明存在以$\overline{\mathbb E}$为谱集但不为完全谱集的交换算子元组。
英文摘要
We determine the cotangent operator space structure at the origin of the tetrablock (denoted by $\mathbb E$). In particular we prove that $\operatorname{COT}_0(\overline{\mathbb E}) =\operatorname{MIN}(\ell_1^2\oplus_\infty\mathbb C)$ completely isometrically. This shows the existence of commuting tuple of operators having $\overline{\mathbb E}$ as a spectral set but not as a complete spectral set.
Comments14 pages. Comments are welcome
