Tensor algebras and displacement structure. II. Noncommutative Szego polynomials

Riesz and Szegö type factorizations for noncommutative Hardy spaces

Let $\A$ be a finite subdiagonal algebra in Arveson's sense. Let $H^p(\A)$ be the associated noncommutative Hardy spaces, $0<p\le\8$. We extend to the case of all positive indices most recent results about these spaces, which include notably the Riesz, Szegö and inner-outer type factorizations. One new tool of the paper is the contractivity of the underlying conditional expectation on $H^p(\A)$ for $p<1$.

Tensor Algebras and Displacement Structure. III. Asymptotic properties

We continue to investigate some classes of Szegö type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szegö to this setting.

行球上的非交换 Szegő 型定理

A Noncommutative Szegő-Type Theorem on the Row-Ball

本文借助非交换测度与 Schur 参数理论，建立 nc 测度和多 Toeplitz 核的对应，证明行球上的非交换 Szegő 型定理及正交多项式零点定理。

Noncommutative function theory and unique extensions

We generalize to the setting of Arveson's maximal subdiagonal subalgebras of finite von Neumann algebras, the Szegö $L^p$-distance estimate, and classical theorems of F. and M. Riesz, Gleason and Whitney, and Kolmogorov. In so doing, we are finally able to provide a complete noncommutative analog of the famous cycle of theorems characterizing the function theoretic generalizations of $H^\infty$. A sample of our other results: we prove a Kaplansky density result for a large class of these algebras, and give a necessary condition for when every completely contractive homomorphism on a unital sub…

A note on noncommutative interpolation

In this paper we formulate and solve Nevanlinna-Pick and Carathéodory type problems for tensor algebras with data given on the N-dimensional operator unit ball of a Hilbert space. We develop an approach based on the displacement structure theory.

谱截断谱三元组上的非交换积分，以及与量子遍历性的关联

A noncommutative integral on spectrally truncated spectral triples, and a link with quantum ergodicity

本研究针对谱截断谱三元组提出非交换积分的简单近似，推导得到非交换几何的Szegő极限公式，建立其与态密度的关联，提出紧谱三元组测地流遍历性的定义，揭示量子遍历性与Connes积分公式的紧密联系。