Journal of Operator Theory

Volume 44, Issue 2, Fall 2000 pp. 347-368.

Unitaire pseudo-multiplicatif associe a un groupoide. Applications a la moyennabilite

Authors: Jean-Michel Vallin
Author institution: Universite d'Orleans, UMR/CNRS 6628 MAPMO, B.P. 6739, F--45067 Orleans Cedex 2, France

Summary: From every measured groupoid, we construct a ``pseudo-multipli\-cative" unitary, which generates the two Hopf-von-Neumann bimodule structures constructed in a former paper, and generalize in this way the well-known multiplicative unitary associated with a locally compact group. We prove a generalization of Leptin theorem which connects the amenability of a measured groupoid and the existence of an approximate unit for its Fourier algebra.

Keywords: Groupoids, multiplicative unitaries, amenability

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