Cyclic Hilbert spaces and Connes' embedding problem

الأصل · EN

Let M be a II₁-factor with trace τ, the linear subspaces of L²(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 L²(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.