投影刻画与对称性自举在近交换算子中的应用
Applications of the Projection Characterization and Symmetry Bootstrap for Operators that are Nearby Commuting Operators
AI总结：
本文利用投影刻画与对称性自举方法，为近交换酉算子、几乎反交换自伴算子及有理相位近交换酉算子证明了新的稳定性定理，并补充了渐近估计。
AI中文摘要：
本文应用arXiv:2412.20795中关于两个算子$A, B$（其中$A$为酉算子或自伴算子）邻近交换算子$A', B'$（其中$A'$为酉算子或自伴算子）的投影刻画与对称性自举，来解决与结构化近交换酉算子、几乎反交换的自伴算子以及近乎交换至有理相位酉算子相关的问题。我们证明了这些矩阵关系类型的若干新稳定性定理。我们还为几个先前缺乏渐近估计的已知稳定性定理提供了构造算子接近程度的估计。
英文摘要：
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.
