Centers of $C^*$-algebras rich in modular ideals

The Fell topology and the modular Gromov-Hausdorff propinquity

Given a unital AF-algebra $A$ equipped with a faithful tracial state, we equip each (norm-closed two-sided) ideal of $A$ with a metrized quantum vector bundle structure, when canonically viewed as a module over $A$, in the sense of Latrémolière using previous work of the first author and Latrémolière. Moreover, we show that convergence of ideals in the Fell topology implies convergence of the associated metrized quantum vector bundles in the modular Gromov-Hausdorff propinquity of Latrémolière. In a similar vein but requiring a different approach, given a compact metric space $(X,d)$, we equip…

Ideals in Operator Space Projective Tensor Product of $C^*$-algebras

For $C^*$-algebras $A$ and $B$, we prove the slice map conjecture for ideals in the operator space projective tensor product $A \hat\otimes B$. As an application, a characterization of prime ideals in the Banach $\ast$-algebra $A\hat\otimes B$ is obtained. Further, we study the primitive ideals, modular ideals and the maximal modular ideals of $A\hat\otimes B$. It is also shown that the Banach $\ast$-algebra $A\hat\otimes B$ possesses Wiener property; and that, for a subhomogenous $C^*$-algebra $A$, $A\hat\otimes B$ is symmetric.

A new approach to recent constructions of C*-algebras from modular index theory

We present a new approach to C*-algebras recently constructed in the context of modular index theory by Carey, Phillips, Putnam and Rennie. It turns out that their constructions can be identified with full corners of ideals in semigroup C*-algebras. This new point of view leads to a systematic analysis of these algebras and their canonical maximal abelian subalgebras.

连续套代数II的稳定理想

The Stable Ideals of a Continuous Nest Algebra II

我们继续研究一个连续套代数的丰富的范数闭，自同构不变理想的家庭。首先，我们提出了一个统一的框架，捕捉所有稳定的理想作为对角压缩极限的内核。然后，我们的特点时，两个这样的限制产生相同的理想，我们得到的详细信息的结构和理想的交集。

乘子拓扑的丰富格结构

Rich lattices of multiplier topologies

该研究证明对称赋范理想诱导的乘子拓扑可反映理想包含关系，以双参数洛伦兹理想为例得到全序不同拓扑链，拓展了相关拓扑的连续族认知。