ar X iv : 0 70 5 . 34 32 v 2 [ m at h . O A ] 1 3 N ov 2 00 7 Reiter ’ s property ( P 1 ) for locally compact quantum groups
نویسنده
چکیده
Let G be a locally compact group. Then G is known to be amenable if and only if it has Reiter’s property (P1), i.e., there is a net (mα)α of non-negative norm one functions in L(G) such that limα supx∈K ‖Lx−1mα−mα‖ = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x). We give a formulation of property (P1) that extends naturally to locally compact quantum groups in the sense of J. Kustermans and S. Vaes, and we show that a locally compact quantum group is amenable if and only if it has (P1).
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