论文标题
非交通理性的克拉克措施
Non-commutative rational Clark measures
论文作者
论文摘要
我们表征了非交通性的Aleksandrov- clark措施和最小的合同的实现公式，尤其是Fock空间的等距非交换性乘数。在这里，$ \ mathbb {c} ^d $上的完整的fock空间被定义为几个非交换形式变量中的Square Square Space of Square Space of Square Space，我们将此空间解释为在复杂单元中的Square-ummable taylor系列中耐强度的耐用空间。我们进一步获得了非交通和承包合理乘数的Aleksandrov- clark量度理论的几种经典结果的类似物。 非共同度量的定义为在Cuntz-toeplitz代数的某个自相关子空间上的正线性功能，这是Unital $ C^* - $ $ c^* - $ $代数由左创建算子在完整的Fock空间上产生的。我们的结果表明，NC Hardy空间理论，Cuntz-Toeplitz和Cuntz代数的表示理论与非交通合理函数的新兴领域之间存在基本关系。
We characterize the non-commutative Aleksandrov--Clark measures and the minimal realization formulas of contractive and, in particular, isometric non-commutative rational multipliers of the Fock space. Here, the full Fock space over $\mathbb{C} ^d$ is defined as the Hilbert space of square--summable power series in several non-commuting formal variables, and we interpret this space as the non-commutative and multi-variable analogue of the Hardy space of square--summable Taylor series in the complex unit disk. We further obtain analogues of several classical results in Aleksandrov--Clark measure theory for non-commutative and contractive rational multipliers. Non-commutative measures are defined as positive linear functionals on a certain self-adjoint subspace of the Cuntz--Toeplitz algebra, the unital $C^*-$algebra generated by the left creation operators on the full Fock space. Our results demonstrate that there is a fundamental relationship between NC Hardy space theory, representation theory of the Cuntz--Toeplitz and Cuntz algebras, and the emerging field of non-commutative rational functions.
