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Interpolation by type I factors and the flip automorphism

1983
1 page
Published in:
  • J.Funct.Anal. 51 (1983) 361-371
DOI:
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Abstract: (Elsevier)
Given two von Neumann algebras A ⊂ B we study the relation between the existence of an interpolating type I factor F , namely A ⊂ F ⊂ B , the implementability of the flip automorphism of A ⊗ A by a unitary in B ⊗ B , and the statistical independence of A and B ′ ( A and B ′ generate a W ∗ -tensor product). As an application in Q.F.T. we derive in a natural way a structure theorem of Buchholz for the von Neumann algebras of local observables associated to free fields.