Approximation property of $C^*$-algebraic Bundles

Amenability, Nuclearity and Tensor Products of $C^{\ast}$-Algebraic Fell Bundles under the Unified Viewpoint of the Fell-Doran Induced Representation Theory

In this paper we study amenability, nuclearity and tensor products of $C^{\ast}$-Fell bundles by the method of induced representation theory.

关于群状C*-代数的普遍性质。II. Fell包

A universal property for groupoid C*-algebras. II. Fell bundles

本文研究Hausdorff局部紧群状上的可能不饱和上半连续Fell包，建立其完整截面C*-代数在任意C*-代数上的表示的普遍性质，并证明其函子性和精确性，定义准轨道空间和映射，扩展Renault的积分与分解定理。

精确性与具有逼近性质的Fell包 over逆半群

Exactness and Fell bundles with the approximation property over inverse semigroups

本文研究了具有逼近性质的Fell包 over逆半群的减少横截代数的精确性，证明其等价于Fell包的单位纤维的精确性，并扩展了作者关于局部紧豪斯多夫第二可数群oid作用于可分C*-代数的结果。

Twisted Partial Actions, A Classification of Stable C*-Algebraic Bundles (Preliminary Version)

We introduce the notion of continuous twisted partial actions of a locally compact group on a C*-algebra. With such, we construct an associated C*-algebraic bundle called the semidirect product bundle. Our main theorem shows that, given any C*-algebraic bundle which is second countable and whose unit fiber algebra is stable, there is a continuous twisted partial action of the base group on the unit fiber algebra, whose associated semidirect product bundle is isomorphic to the given one.

Amenability for actions of étale groupoids on $C^*$-algebras and Fell bundles

We generalize Renault's notion of measurewise amenability to actions of second countable, Hausdorff, étale groupoids on separable $C^*$-algebras and show that measurewise amenability characterizes nuclearity of the crossed product whenever the $C^*$-algebra acted on is nuclear. In the more general context of Fell bundles over second countable, Hausdorff, étale groupoids, we introduce a version of Exel's approximation property. We prove that the approximation property implies nuclearity of the cross-sectional algebra whenever the unit bundle is nuclear. For Fell bundles associated to groupoid a…

具有小边界性质的最小线束扭曲同胚的C*-代数的Z稳定性

$\mathcal{Z}$-stability for $\mathrm C^*$-algebras of minimal line-bundle-twisted homeomorphisms with the small boundary property

本文研究了具有小边界性质的最小线束扭曲同胚的C*-代数的Z稳定性，并展示了其分类及张量积的稳定性。