The unitary implementation of a measured quantum groupoid action (Q617044)

This paper is a continuation of the author's Memoir [Mém. Soc. Math. Fr., Nouv. Sér. 114, 1--150 (2008; Zbl 1189.58002)]. The main purpose is to address two issues left unresolved in that paper. Firstly, one wants a standard implementation of a locally compact quantum groupoid and secondly a biduality theorem for weights. The first result had been obtained for locally compact quantum groups by S.~Vaes, the second for measured groupoids by T.~Yamanouchi. The author proves both results here under the assumption that there is a faithful normal semifinite weight of the von Neumann algebra \(M\) on which the measured quantum groupoid acts onto the copy of the basis of the measured quantum groupoid inside \(M\).