\(L^2\)-von Neumann modules, their relative tensor products and the spatial derivative (Q1977662)

From author's abstract: We develop a theory of \(L^2\)-von Neumann modules, which encompasses a reformulation of Connes' spatial derivative, and the relative tensor product of Sauvageot. We demonstrate the naturality of the relative tensor product construction in the category of \(L^2\)-von Neumann bimodules. Finally, we give evidence for the claim that the relative tensor product is essentially the only tensor product which should be used when considering this tensor category.