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Cyclic Hilbert Spaces and Connes’ Embedding Problem

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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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Authors and Affiliations

  1. University of Rome “Tor Vergata”, Rome, Italy

    Valerio Capraro & Florin Rădulescu

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  1. Valerio Capraro
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  2. Florin Rădulescu
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Correspondence to Valerio Capraro.

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Communicated by Ilan Hirshberg.

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Capraro, V., Rădulescu, F. Cyclic Hilbert Spaces and Connes’ Embedding Problem. Complex Anal. Oper. Theory 7, 863–872 (2013). https://doi.org/10.1007/s11785-011-0188-4

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