论文标题
支持扩展$ \ mathrm c^*$ - 代数
Support expansion $\mathrm C^*$-algebras
论文作者
论文摘要
我们在$ l^2 $空间上考虑运算符，以通过某些约束功能控制的方式扩展向量的支持。研究的主要对象是$ \ mathrm c^*$ - 由合适的约束家庭产生的代数，我们称之为支持扩展$ \ mathrm c^*$ - 代数。在离散设置中，支持扩展$ \ MATHRM C^*$ - 代数是经典的ROE代数，此处的连续版本提供了“可测量”或“量子”统一ROE代数的示例，这些代数在同伴论文中开发。我们发现，与离散设置相反，支持扩展的poset $ \ mathrm c^*$ - $ \ mathcal b（l^2（\ mathbb r））$内部的代数非常富裕，具有无法占上风的上升链，降链，下降链和抗抗心。
We consider operators on $L^2$ spaces that expand the support of vectors in a manner controlled by some constraint function. The primary objects of study are $\mathrm C^*$-algebras that arise from suitable families of constraints, which we call support expansion $\mathrm C^*$-algebras. In the discrete setting, support expansion $\mathrm C^*$-algebras are classical uniform Roe algebras, and the continuous version featured here provides examples of "measurable" or "quantum" uniform Roe algebras as developed in a companion paper. We find that in contrast to the discrete setting, the poset of support expansion $\mathrm C^*$-algebras inside $\mathcal B(L^2(\mathbb R))$ is extremely rich, with uncountable ascending chains, descending chains, and antichains.
