Un critère de rationalité provenant de la géométrie non commutative

  title={Un crit{\`e}re de rationalit{\'e} provenant de la g{\'e}om{\'e}trie non commutative},
  author={G{\'e}rard Duchamp and Christophe Reutenauer},
  journal={Inventiones mathematicae},
We prove a conjecture of A. Connes, which gives a rationality criterion for elements of the closure of ℂΓ (Γ a free group) in the space of bounded operators in l2(Γ). We show that this criterion applies also to the ring of Malcev-Neumann series on Γ. 

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