A short note on Multilevel Toeplitz Matrices

Holomorphic functions on the symmetrized bidisk II -- Interpolating sequences and the Toeplitz corona theorem

This note contains two new theorems about bounded holomorphic functions on the symmetrized bidisk -- a characterization of interpolating sequences and a Toeplitz corona theorem.

带有单项式符号的Toeplitz算子的交换子

Commutants of Toeplitz operators with monomial symbols

本文描述了完备强伪凸Reinhardt整环上的Toeplitz代数中乘法算子与单项式的交换子。

Bergman空间上解析Toeplitz算子的交换子

Commutants of Analytic Toeplitz Operators on the Bergman Space

本文证明了如果Bergman空间上的两个Toeplitz算子可交换，且其中一个算子的符号是解析的且是非常数的，则另一个算子也是解析的.

The operator system of Toeplitz matrices

A recent paper of A.~Connes and W.D.~van Suijlekom identifies the operator system of $n\times n$ Toeplitz matrices with the dual of the space of all trigonometric polynomials of degree less than $n$. The present paper examines this identification in somewhat more detail by showing explicitly that the Connes--van Suijlekom isomorphism is a unital complete order isomorphism of operator systems. Consequences of this complete order isomorphism are also examined, yielding two special results of note: (i) that every positive linear map of the $n\times n$ complex matrices is completely positive when …

单位圆盘Hardy空间上Toeplitz算子的动力学性质导论

Introduction To The Dynamical Properties Of Toeplitz Operators On The Hardy Space Of The Unit Disc

本文基于2025年ACOTCA会议的迷你课程笔记，以初学者可理解的方式给出超循环Toeplitz算子前两个关键结果的完整证明。

关于半Fredholm Hilbert模的一个注记

A note on semi-Fredholm Hilbert modules

算子理论中的一个经典问题是确定C^m中开单位球上的向量值全纯函数的希尔伯特空间上的Toeplitz型算子的谱。在本文中，我们获得了此类算子的k-元组成为泰勒意义下的Fredholm的必要条件，并证明它们在单位圆盘的情况下是充分的。

Point spectrum and hypercyclicity problem for a class of truncated Toeplitz operators

In this note we discuss an open problem whether a truncated Toeplitz operator on a model space can be hypercyclic. We compute point spectrum and eigenfunctions for a class of truncated Toeplitz operators with polynomial analytic and antianalytic parts. We show that, for a class of model spaces, truncated Toeplitz operators with symbols of the form $Φ(z) =a \bar{z} +b + cz$, $|a| \ne |c|$, have complete sets of eigenvectors, and, in particular, are not hypercyclic.

关于双圆盘 Bergman 空间上 Toeplitz 算子本质谱的研究

On the essential spectra of Toeplitz operators on Bergman spaces of the bi-disc

本文研究双圆盘 Bergman 空间上符号为连续函数的 Toeplitz 算子的本质谱确定问题，给出了相应本质谱的刻画。

四面体块的Brown-Halmos型刻画

Brown-Halmos type characterization for the tetrablock

本文建立了四面体块Hardy空间上Toeplitz算子的Brown-Halmos型刻画，并由此证明零算子是唯一的紧Toeplitz算子。

A note on convexity of sections of quaternionic numerical range

The quaternionic numerical range of matrices over the ring of quaternions is not necessarily convex. We prove Toeplitz-Hausdorff like theorem, that is, for any given quaternionic matrix every section of its quaternionic numerical range is convex. We provide some additional equivalent conditions for the quaternionic numerical range of matrices over quaternions to be convex and prove some numerical radius inequalities.

Fixed point theorem for an infinite Toeplitz matrix and its extension to general infinite matrices

In [V. M. Abramov, \emph{Bull. Aust. Math. Soc.} \textbf{104} (2021), 108--117] the fixed point equation for an infinite nonnegative Toeplitz matrix has been studied. It was found the conditions for existence of a positive solution and bounded positive solution. However, the proof of the existence of a positive solution was entirely straightforward, not admitting extensions for more general types of matrices. In the present note, we provide an alternative proof for the existence of a positive solution in more general case. The presented proof is based on an application of a variant of the fixe…

由置换位移生成的Toeplitz矩阵与三角核

Toeplitz matrices from permutation displacements and the triangular kernel

本文研究了通过缩放核a_k=f(k/n)生成的Toeplitz矩阵，证明其特征值均值收敛于f的加权积分，并引入置换位移计数的组合构造，最终分析了与置换位移相关的极限谱结构。

Generalized Anti-Wick Quantum States

The purpose of this Note is to study a simple class of mixed states and the corresponding density operators (matrices). These operators, which we call quite Toeplitz density operators correspond to states obtained from a fixed function ("window") by position-momentum translations, and reduce in the simplest case to the anti-Wick operators considered long ago by Berezin. The rigorous study of Toeplitz operators requires the use of classes of functional spaces defined by Feichtinger.