Reiter ’ s property ( P 1 ) for locally compact quantum groups

Reiter’s Properties for the Actions of Locally Compact Quantum Goups on von Neumann Algebras

8 A ug 2 00 8 Reiter ’ s properties ( P 1 ) and ( P 2 ) for locally compact quantum groups

A locally compact group G is amenable if and only if it has Reiter’s property (Pp) for p = 1 or, equivalently, all p ∈ [1,∞), 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‖p = 0 for each compact subset K ⊂ G (Lx−1mα stands for the left translate of mα by x ). We extend the definitions of properties (P1) and (P2) from locally compact gro...

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

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 i...

Asymptotic invariance properties for locally compact quantum groups

Let G be a locally compact group. Then G is known to be amenable if and only if it satisfies 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 propety (P1) that extends naturally to locally compact quantum groups in ...

One-point extensions of locally compact paracompact spaces

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...