A bounded linear operator A acting on a separable complex Hilbert space H is called C-normal with respect to some conjugation C on H if \(CA^*AC=AA^*\). In the present paper, we show that every bounded linear operator A on H can be perturbed by finite-rank operator F with norm as small as desired so that \(A+F\) is not C-normal with respect to any conjugation C.

中文翻译：

---

非C规范运算符密集

如果\（CA ^ * AC = AA ^ * \）相对于H上的某些共轭C，作用在可分离复希尔伯特空间H上的有界线性算子A称为C-法线。在本文中，我们证明了H上的每个有界线性算子A都可以受到有限秩算子F的扰动，范数与期望的一样小，因此\（A + F \）并非C-关于任何共轭C的法线。