The relative tensor product and a minimal fiber product in the setting of $C^{*}$-algebras

AT-algebras from fiberwise essentially minimal zero-dimensional dynamical systems

We introduce a type of zero-dimensional dynamical system (a pair consisting of a totally disconnected compact metrizable space along with a homeomorphism of that space), which we call "fiberwise essentially minimal", and we prove that the associated crossed product $ C^* $-algebra of such a system is an AT-algebra. Under the additional assumption that the system has no periodic points, we prove that the associated crossed product $ C^* $-algebra has real rank zero, which tells us that such $ C^* $-algebras are classifiable by $ K $-theory. We show that the definition of fiberwise essentially m…

逐纤维本质极小零维动力系统交叉积的动力系统分类

A dynamical classification for crossed products of fiberwise essentially minimal zero-dimensional dynamical systems

本文证明了逐纤维本质极小零维动力系统交叉积的$ K $-理论同构当且仅当系统强轨道等价，并在无周期点条件下给出了包含$ C^* $-代数同构的分类定理。

A note on the minimal tensor product and the C*-envelope of operator systems

In this article, we show that the $C^*$-envelope of the minimal tensor product of two operator systems is isomorphic to the minimal tensor product of their $C^*$-envelopes. We do this by identifying the Silov boundary ideal of the minimal tensor product of two operator systems. Finally, as an application of this result, we show that the propagation number of the minimal tensor product of operator systems is the maximum of the propagation numbers of the factors.

子乘积系统的张量代数与非交换函数论

Tensor algebras of subproduct systems and noncommutative function theory

本文重新研究无限维纤维子乘积系统的张量代数，刻画其可识别为非交换齐次簇上一致连续非交换函数代数的条件，指出无限维纤维情形下零点定理可能不成立，并解决了其同构问题。

Topological properties of spaces of ideals of the minimal tensor product

One shows that for two C^*-algebras A_1 and A_2 any continuous function on Prim(A_1)\times Prim(A_2) can be continuously extended to Prim(A_1\otimes A_2) provided it takes its values in a T_1 topological space. This generalizes a 1977 result of L.G. Brown. A new proof is given for a result of R.J. Archbold about the space of minimal primal ideals of A_1\otimes A_2. To obtain these two results one makes use of the topological properties of the space of prime ideals of the minimal tensor product.