We analyze the algebraic structure of the Connes fusion tensor product (CFTP) in the case of bi-finite Hilbert modules over a von Neumann algebra M. It turns out that all complications in its definition disappear if one uses the closely related bi-modules of bounded vectors. We construct an equivalence of monoidal categories with duality between a category of Hilbert bi-modules over M with CFTP and some natural category of bi-modules over M with the usual relative algebraic tensor product.
Keywords: Connes fusion tensor product, von Neumann algebras
2000 MSC: 46LXX, 16DXX
Theory and Applications of Categories, Vol. 25, 2011, No. 2, pp 38-50.
Published 2011-02-08.
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