Ramezanpour, M.; Vishki, H. R. Ebrahimi Reiter’s properties for the actions of locally compact quantum groups on von Neumann algebras. (English) Zbl 1251.43002 Bull. Iran. Math. Soc. 36, No. 2, 1-17 (2010). Daws and Runde introduced the Reiter’s conditions \(P_1\) and \(P_2\) for a general locally compact quantum group. The authors present a slightly different approach to study these conditions for the action of a locally compact quantum group on a von Neumann algebra. In particular they show that the action has Reiter’s condition \(P_1\) if and only if it is left amenable and Reiter’s condition \(P_2\) if and only if the corresponding unitary corepresentation (which implements the action) has the weak containment property. Reviewer: Massoud Amini (Tehran) MSC: 43A07 Means on groups, semigroups, etc.; amenable groups 22F05 General theory of group and pseudogroup actions 22D10 Unitary representations of locally compact groups 46L07 Operator spaces and completely bounded maps 46L65 Quantizations, deformations for selfadjoint operator algebras 46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 81R15 Operator algebra methods applied to problems in quantum theory 46L55 Noncommutative dynamical systems 11Y50 Computer solution of Diophantine equations Keywords:locally compact quantum group; action; unitary corepresentation; amenability; Hopf-von Neumann algebra; Reiter property PDFBibTeX XMLCite \textit{M. Ramezanpour} and \textit{H. R. E. Vishki}, Bull. Iran. Math. Soc. 36, No. 2, 1--17 (2010; Zbl 1251.43002) Full Text: arXiv