非单 C*-代数张量积的 Pedersen 理想
Pedersen ideals of tensor products of nonunital C*-algebras
AI总结：
本文证明了非单 C*-代数张量积的 Pedersen 理想中正元素可通过正元素张量积的和强逼近，并应用于确定迹锥、Cuntz-Pedersen 空间及计算 Cuntz 半群等结构。
摘要：
我们证明了张量积的 Pedersen 理想中的正元素，可以通过正元素张量积的和以一种特别强的意义进行逼近。这对迹锥及相关主题的结构有诸多应用，例如 Cuntz-Pedersen 空间或 Cuntz 半群。例如，我们根据张量因子的迹，在任意 C*-张量范数下确定了张量积的下半连续迹的锥。我们证明了 Pedersen 理想的正元素在 Cuntz 等价下有时是稳定的。我们推广了 Pedersen 的一个结果，证明了某些类的完全正映射将一个 Pedersen 理想映射到另一个 Pedersen 理想中。我们提供了在许多情况下计算张量积 Cuntz 半群的定理。
英文摘要：
We show that positive elements of a Pedersen ideal of a tensor product can be approximated in a particularly strong sense by sums of tensor products of positive elements. This has a range of applications to the structure of tracial cones and related topics, such as the Cuntz-Pedersen space or the Cuntz semigroup. For example, we determine the cone of lower semicontinuous traces of a tensor product in terms of the traces of the tensor factors, in an arbitrary C*-tensor norm. We show that the positive elements of a Pedersen ideal are sometimes stable under Cuntz equivalence. We generalize a result of Pedersen's by showing that certain classes of completely positive maps take a Pedersen ideal into a Pedersen ideal. We provide theorems that in many cases compute the Cuntz semigroup of a tensor product.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
