Non-commutative Clark measures for the free and Abelian Toeplitz algebras
Non-commutative Clark measures for the free and Abelian Toeplitz algebras
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自由代数和阿贝尔托普利茨代数的非交换克拉克测度
DOI：
10.1016/j.jmaa.2017.07.023
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发表时间：
2017
影响因子：
1.3
通讯作者：
R. Martin
中科院分区：
文献类型：
--
作者：
M. Jury;R. Martin
对Cd上的向量值满Fock空间的自由Toeplitz代数的闭单位球，算子值自由Schur类中的任意元素构造了一个非交换的Aleksandrov-Clark测度.这里，自由（解析）Toeplitz代数是由自由移位的分量算子生成的单位弱算子拓扑（WOT）-闭代数，左创建算子的行等距。这定义了自由算子值Schur类和自由圆盘代数的算子系统上的完全正映射（非交换AC测度）之间的双射，自由圆盘代数是由自由移位生成的范数闭代数。将Drury-Arveson空间与对称Fock空间等同起来，确定了算子值交换Schur类（由Arveson移位生成的WOT-闭Toeplitz代数的闭单位球）元素的非交换AC测度与其自由提升到自由Schur类的AC测度之间的关系.
We construct a non-commutative Aleksandrov–Clark measure for any element in the operator-valued free Schur class, the closed unit ball of the free Toeplitz algebra of vector-valued full Fock space over C d. Here, the free (analytic) Toeplitz algebra is the unital weak operator topology (WOT)-closed algebra generated by the component operators of the free shift, the row isometry of left creation operators. This defines a bijection between the free operator-valued Schur class and completely positive maps (non-commutative AC measures) on the operator system of the free disk algebra, the norm-closed algebra generated by the free shift. Identifying Drury–Arveson space with symmetric Fock space, we determine the relationship between the non-commutative AC measures for elements of the operator-valued commutative Schur class (the closed unit ball of the WOT-closed Toeplitz algebra generated by the Arveson shift) and the AC measures of their free liftings to the free Schur class.
非交换再生核希尔伯特空间
DOI：
10.1016/j.jfa.2016.06.010
发表时间：
1920
期刊：
arXiv: Operator Algebras
影响因子：
--
作者：
J.A. Ball;G. Marx;V. Vinnikov
通讯作者：
V. Vinnikov