Complex symmetry operators have notable applications in extension and dilation results, rank one perturbations of Jordan operators, matrix-valued inner functions and free interpolation theory in the disk and so on. While in the study of the complex symmetric operators, one of the problems one always encounters is when a C $$^*$$ -algebra singly generated contains no nonzero compact operators. In this paper, we answer this question recur to matrix weighted shift operators.

中文翻译：

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由矩阵加权移位生成的 C$$^*$$-代数中的紧凑运算符

复对称算子在扩展和膨胀结果、Jordan算子的一阶摄动、矩阵值内函数和圆盘中的自由插值理论等方面有着显着的应用。而在研究复对称算子时，经常遇到的问题之一是当一个单独生成的C $$^*$$ -代数不包含非零紧算子时。在本文中，我们通过矩阵加权移位运算符来回答这个问题。