Dual truncated Toeplitz operators and other restrictions of the multiplication by the independent variable $$M_z$$ on the classical $$L^2$$ space on the unit circle are investigated. Commutators are calculated and commutativity is characterized. A necessary and sufficient condition for any operator to be a dual truncated Toeplitz operator is established. A formula for recovering its symbol is stated.

中文翻译：

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乘法运算符的压缩及其特征

研究了单位圆上经典$$L^2$$空间上自变量$$M_z$$乘法的双重截断Toeplitz算子和其他限制。计算交换器并表征交换性。建立了任何算子是双截断托普利兹算子的充要条件。给出了恢复其符号的公式。