EVERY TOPOLOGICALLY AMENABLE LOCALLY COMPACT QUANTUM GROUP IS AMENABLE

P-Amenable Locally Compact Hypergroups

p-amenable locally compact hypergroups

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TOPOLOGICALLY STATIONARY LOCALLY COMPACT SEMIGROUP AND AMENABILITY

In this paper, we investigate the concept of topological stationary for locally compact semigroups. In [4], T. Mitchell proved that a semigroup S is right stationary if and only if m(S) has a left Invariant mean. In this case, the set of values ?(f) where ? runs over all left invariant means on m(S) coincides with the set of constants in the weak* closed convex hull of right translates of f. Th...

Amenable Groups with a Locally Invariant Order Are Locally Indicable

We show that every amenable group with a locally invariant partial order has a left-invariant total order (and is therefore locally indicable). We also show that if a group G admits a left-invariant total order, and H is a locally nilpotent subgroup of G, then a left-invariant total order on G can be chosen so that its restriction to H is both left-invariant and right-invariant. Both results fo...

Fourier and Figà-Talamanca–Herz algebras on amenable, locally compact groups

For a locally compact group G, let A(G) denote its Fourier algebra and, for p ∈ (1,∞), let Ap(G) be the corresponding Figà-Talamanca–Herz algebra. For amenable G and p, p ∈ (1,∞) such that 1 p + 1 p , we show that Ap(G) ∩Ap′(G) = A(G).