Algèbres de von Neumann finies ayant la propriété de Haagerup et semi-groupes L2-compacts

Abstract

The goal of this note is to characterize Haagerup property for finite von Neumann algebras in terms of $||.||_{2}$-continuous semi-group of completely positive $L^{2}$-compact maps. The generator of this semi-group could be interpreted as an analogue for von Neumann algebras having the Haagerup property of a proper conditionally negative definite map on a group having Haagerup property.