论文标题
Q分组的Q模型
Models for q-commutative tuples of isometries
论文作者
论文摘要
一对希尔伯特太空线性操作员$（v_1，v_2）$据说为$ q $ - 交换性，对于单模型的复杂数字$ q $，如果$ v_1v_2 = qv_2v_1 $。获得了$ Q $ - 交换性异构体的混凝土功能模型。功能模型通过作用于它们的希尔伯特空间和操作员的集合来参数。结果，该系列是$ Q $交换性异构体的完全单一不变性。 A $ Q $ - 交通运算符$（v_1，v_2）$被认为是双重$ q $ - 交换性的，如果此外，它满足$ v_2v_1^*= qv_1^*v_2 $。还表征了$ q $ q $ - 共同的异构体。特别注意$ Q $ Q $ - 交换运算符的双对。然后，$ q $ - 征收的概念自然扩展到了一般的操作员的情况下，以获取类似的$ q $ - c $ - 交换异构体的模型。
A pair of Hilbert space linear operators $(V_1,V_2)$ is said to be $q$-commutative, for a unimodular complex number $q$, if $V_1V_2=qV_2V_1$. A concrete functional model for $q$-commutative pairs of isometries is obtained. The functional model is parametrized by a collection of Hilbert spaces and operators acting on them. As a consequence, the collection serves as a complete unitary invariance for $q$-commutative pairs of isometries. A $q$-commutative operator pair $(V_1,V_2)$ is said to be doubly $q$-commutative, if in addition, it satisfies $V_2V_1^*=qV_1^*V_2$. Doubly $q$-commutative pairs of isometries are also characterized. Special attention is given to doubly $q$-commutative pairs of shift operators. The notion of $q$-commutativity is then naturally extended to the case of general tuples of operators to obtain a similar model for tuples of $q$-commutative isometries.
