A characterization of rationality in free semicircular operators
A characterization of rationality in free semicircular operators
复制标题
自由半圆算子有理性的表征
DOI：
10.1016/j.jfa.2022.109609
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发表时间：
2022
影响因子：
1.7
通讯作者：
Miyagawa Akihiro
中科院分区：
文献类型：
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作者：
Miyagawa Akihiro
对于在全Fock空间上实现的自由半圆元，证明了由它们得到的算子的合理性与它们的右零化算子的秩的有限性之间的等价性.这与G关于自由群的约化C-代数的结果类似。Duchamp和C.由PA Linnell扩展到与自由群因子相关的稠密定义的无界算子。虽然他们的结果是由量子化微积分在非交换几何的动机，我们陈述我们的结果的自由概率论。
For free semicircular elements realized on the full Fock space, we prove an equivalence between rationality of operators obtained from them and finiteness of the rank of their commutators with right annihilation operators. This is an analogue of the result for the reduced C⁎-algebra of the free group by G. Duchamp and C. Reutenauer which was extended by PA Linnell to densely defined unbounded operators affiliated with the free group factor. While their result was motivated by quantized calculus in noncommutative geometry, we state our results in terms of free probability theory.