Let M be a II 1 -factor with trace τ, the finite dimensional subspaces of L 2 (M, τ) are not just common Hilbert spaces, but they have an additional structure. We introduce the notion of a cyclic linear space by taking these additional properties as axioms. In Sect. 3 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 Sect. 4 we make a first step towards the answer of the previous question.
Capraro, V., Radulescu, F. (2013). Cyclic Hilbert spaces and Connes' embedding problem. COMPLEX ANALYSIS AND OPERATOR THEORY, 7(4), 863-872 [10.1007/s11785-011-0188-4].
Cyclic Hilbert spaces and Connes' embedding problem
Capraro V
;
2013
Abstract
Let M be a II 1 -factor with trace τ, the finite dimensional subspaces of L 2 (M, τ) are not just common Hilbert spaces, but they have an additional structure. We introduce the notion of a cyclic linear space by taking these additional properties as axioms. In Sect. 3 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 Sect. 4 we make a first step towards the answer of the previous question.
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