Motivated by results in uniform algebras, a distance localization formula in C*-algebras is established in the framework of the Allan–Douglas localization principle, and is used to derive a locality result for products of Hankel operators as compact perturbations of Hankel operators. Using localization and certain QC functions, it is proved that the essential spectrum of the commutator of a Toeplitz and a Hankel operator is antipodal symmetric under a mild condition on the Hankel symbol function. Under the same condition the essential spectrum of a Hankel operator also exhibits this symmetry. Conjugates of interpolating Blaschke products and characteristic functions are constructed that satisfy the condition, while examples show the condition is only sufficient.

中文翻译：

---

关于Hankel算子和Toeplitz和Hankel算子的换向子的紧微扰

受均匀代数结果的启发，在Allan-Douglas定域原理的框架内建立了C*-代数中的距离定域公式，用于将汉克算子的乘积作为汉克算子的紧扰动推导出定域结果。利用定位和一定的QC函数，证明了托普利兹和汉克尔算子的换向子的本质谱在汉克尔符号函数的温和条件下是对映对称的。在相同条件下，汉克尔算符的本质谱也表现出这种对称性。构造了满足条件的内插 Blaschke 乘积和特征函数的共轭，而例子表明条件只是充分的。