Algèbres de Kac moyennables

Michel Enock and Jean-Marie Schwartz

Vol. 125 (1986), No. 2, 363–379

DOI: 10.2140/pjm.1986.125.363

Abstract

We generalize the classical theory of amenable locally compact groups to Kac algebras. Most of the equivalent definitions of amenability are translated into the formalism of Kac algebras and still remain equivalent. Among others, we see that every “group dual” (i.e. symmetric Kac algebra) is amenable.

Results on actions of amenable groups on von Neumann algebras are extended as well; this allows us to obtain new properties on group co-actions (i.e. actions of “group duals”).

Mathematical Subject Classification 2000

Primary: 46L55

Secondary: 22D25

Milestones

Received: 21 June 1985

Published: 1 December 1986