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

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

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...

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...

m at h . FA ] 1 8 A ug 2 00 3 Applications of operator spaces to abstract harmonic analysis

We give a survey of how the relatively young theory of operator spaces has led to a deeper understanding of the Fourier algebra of a locally compact group (and of related algebras).

ar X iv : 0 90 5 . 12 96 v 1 [ m at h . O A ] 8 M ay 2 00 9 CONVOLUTION SEMIGROUPS OF STATES

Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we initiate a theory of weakly continuous convolution semigroups of functionals on a C∗bialgebra, the noncommutative counterpart of locally compact semigroup. On locally compact quantum groups we obtain a bijective corres...