三维中的UCP扩张

中文摘要 AI 辅助

我们证明了有限维算子系统的每个UCP扩张问题在有限矩阵放大后可归结为三维问题。扩张的集合通过仿射双射保持不变。矩阵大小约为$\sqrt{d}$阶，其中$d$是原始系统的维数。这也给出了Arveson超刚性猜想的一个三维（最小）反例。

英文摘要

We show that every UCP extension problem for a finite dimensional operator system can be reduced to three dimensions after finite matrix amplification. The set of extensions is preserved by an affine bijection. The matrix size is of order $\sqrt{d}$, where $d$ is the dimension of the original system. This also gives a three dimensional (smallest) counterexample to Arveson's hyperrigidity conjecture.

发表机构

• Mathematical Reviews（数学评论）

机构由 AI 辅助整理，请以论文原文为准。