循环希尔伯特空间与Connes嵌入问题
Cyclic Hilbert spaces and Connes' embedding problem
摘要：
设$M$是一个具有迹$τ$的$II_1$ -因子，$L^2(M,τ)$的线性子空间不仅是普通的希尔伯特空间，而且具有附加结构.我们引入循环线性空间的概念，把这些性质作为公理。在第二节中，我们提出了以下问题：“对于某些$M$，是否每个循环希尔伯特空间都嵌入到$L^2(M,τ)$中？".肯定的回答意味着存在一种算法来检验Connes的嵌入猜想。在第3节中，我们为回答上一个问题迈出了第一步。
英文摘要：
Let $M$ be a $II_1$-factor with trace $τ$, the linear subspaces of $L^2(M,τ)$ are not just common Hilbert spaces, but they have additional structure. We introduce the notion of a cyclic linear space by taking those properties as axioms. In Sec.2 we formulate the following problem: "does every cyclic Hilbert space embed into $L^2(M,τ)$, for some $M$?". An affirmative answer would imply the existence of an algorithm to check Connes' embedding Conjecture. In Sec.3 we make a first step towards the answer of the previous question.
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。
