论文标题
非共同的F＆M Riesz定理
A non-commutative F&M Riesz Theorem
论文作者
论文摘要
我们将复杂单元圆的分析复合物测量的结果扩展到非共同的多元设置。 Identifying continuous linear functionals on a certain self-adjoint subspace of the Cuntz--Toeplitz $C^*-$algebra, the free disk operator system, with non-commutative (NC) analogues of complex measures, we refine a previously developed Lebesgue decomposition for positive NC measures to establish an NC version of the Frigyes and Marcel Riesz Theorem for `analytic' measures, i.e.复杂的措施，消失了积极时刻。证明依靠新的结果取决于我们开发并从经典量度理论延伸的阳性NC测量的顺序属性。
We extend results on analytic complex measures on the complex unit circle to a non-commutative multivariate setting. Identifying continuous linear functionals on a certain self-adjoint subspace of the Cuntz--Toeplitz $C^*-$algebra, the free disk operator system, with non-commutative (NC) analogues of complex measures, we refine a previously developed Lebesgue decomposition for positive NC measures to establish an NC version of the Frigyes and Marcel Riesz Theorem for `analytic' measures, i.e. complex measures with vanishing positive moments. The proof relies on novel results on the order properties of positive NC measures that we develop and extend from classical measure theory.
