Crossed products by groupoid actions and their smooth flows of weights (Q1328883)

In [`Duality for actions and coactions of measured proupoids on vonNeumann algebras', Mem. Am. Math. Soc. 484, 101 p. (1993; Zbl 0822.46070)], the author introduced the notion of an action and a coaction of a measurable groupoid on a von Neumann algebra. He constructed their crossed product, dual (co)action and extended the Nakagami-Takesaki duality theorem. In the present paper the crossed product is realized as the left von Neumann algebra of a left Hilbert algebra. This generalizes known results for the group action to the groupoid setting.