Z-Analytic TAF Algebras and Partial Dynamical Systems

Analytic Partial Crossed Products

Partial actions of discrete abelian groups can be used to construct both groupoid C*-algebras and partial crossed product algebras. In each case there is a natural notion of an analytic subalgebra. We show that for countable subgroups of the real numbers and free partial actions, these constructions yield the same C*-algebras and the same analytic subalgebras. We also show that under suitable hypotheses an analytic partial crossed product preserves all the information in the dynamical system in the sense that two analytic partial crossed products are isomorphic as Banach algebras if, and only …

Analytic aspects of the bi-free partial R-transform

Since Voiculescu introduced his bi-free probability theory in 2013, the major development of the theory has been on its combinatorial side; in particular, on the combinatorics of bi-free cumulants and its application to the bi-free R-transform. In this article we propose a harmonic analysis approach to the bi-free R-transform, which is solely based on integral transforms of two variables. To accommodate the harmonic analysis tools, we confine ourselves in the simplest situation of bi-freeness with commuting faces. Our method allows us to treat measures with unbounded support, and we show that …

幂部分等距的特征函数

Characteristic function of a power partial isometry

本文基于Sz.-Nagy-Foiaş模型理论，完整分类了与c.n.u.幂部分等距关联的纯压缩解析函数，并刻画了使Toeplitz算子成为部分等距的算子值符号。