C* 代数中的序单位

具有序单位的C*-Segal代数

C*-Segal algebras with order unit

引入了（非交换）C*-Segal代数作为C* 代数中稠密理想的巴拿赫代数的概念.研究了C *-Segal代数的几个基本性质，并利用乘子模理论确定了具有序单位的C*-Segal代数的结构.

单位球Bergman空间上Toeplitz代数中Toeplitz算子的密度研究

On the density of Toeplitz operators in the Toeplitz algebra over the Bergman space of the unit ball

该研究采用量子调和分析与表示论方法，给出单位球Bergman空间上Toeplitz代数中Toeplitz算子按范数稠密的夏氏定理的新证明。

Spectral theorem approach to commutative C* -algebras generated by Toeplitz operators on the unit ball: quasi-elliptic related cases

We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which are functions of certain collections of commuting unbounded self-adjoint operators in the Bergman space.

紧量子群C^*-代数作为具有近似单位的霍普夫代数

Compact quantum group C^*-algebras as Hopf algebras with approximate unit

本文构造并研究了具有近似单位的Hopf C^*-代数的表示论，它构成了紧群C^*-代数的量子模拟.首先在任意的具有积分的霍普夫代数H上引入卷积积，然后当H是紧的Hopf *-代数时，利用新的卷积积构造H的L_2和C^*-包络.

C*-Algebras With and Without $\ll$-Increasing Approximate Units

For elements $a, b$ of a C*-algebra we denote $a=ab$ by $a\ll b$. We show that all $ω_1$-unital C*-algebras have $\ll$-increasing approximate units, extending a classical result for $σ$-unital C*-algebras. We also construct (in ZFC) the first examples of C*-algebras with no $\ll$-increasing approximate unit. One of these examples is a C*-subalgebra of $\mathcal B(\ell_2(ω_1))$. These examples are, by necessity, not approximately finite dimensional (AF), but some of them are still scattered and so locally finite dimensional (LF) in the sense of Farah and Katsura. It follows that there are scatt…

作为层的Etale广群代数上的模

Modules over etale groupoid algebras as sheaves

作者以前已经把具有单位$\Bbbk$的交换环和具有局部紧的Hausdorff全不连通的单位空间的Etale广群$\mathscr G$与一个$\Bbbk$ -代数$\Bbbk\mathscr G$联系起来。代数$\Bbbk\mathscr G$不必是单位的，但它总是有局部单位。广群代数类包括群代数、逆半群代数和Leavitt路代数。本文证明了酉$\Bbbk\mathscr G$ -模范畴等价于$\mathscr G$上$\Bbbk$ -模层范畴.作为结果，我们得到了一个新的证明最近的结果，森田等价群胚有森田等价代数。