Cyclic Hilbert spaces and Connes' embedding problem

Abstract

Let $M$ be a $I{I}_1$-factor with trace $\tau$, the linear subspaces of $L^2(M,\tau )$ 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 $L^2(M,\tau )$, 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.

References in corpus (1)

• A Linearization of Connes' Embedding Problem