Amenability and ideals in A(G)

Abstract

Closed ideals in

On a separation property of positive definite functions on locally compact groups

“…Also, slightly generalizing the result of [5] mentioned above, it was shown in [10] that G has the H-separation property whenever H is a neutral subgroup of G. Here a subgroup H is called neutral if given any neighbourhood U of the identity, there exists a neighbourhood V of the identity such that V H ⊆ HU . Such subgroups were first considered in [16] in the context of invariant measures on homogeneous spaces and have later been studied extensively in [13] (see also [17]).…”

“…When G has the H-separation property for each closed subgroup H of G, we call G a group with the separation property. The H-separation property first appeared in [12] where it was noticed that it is satisfied if H is either normal, or compact, or open in G. Moreover, every SIN-group (that is, a group with small conjugation invariant neighbourhoods of the identity) has the separation property [5]. The interest in and importance of the H-separation property arises from the fact that it turned out to be useful in studying the ideal theory of the Fourier algebra A(G) (see [10]).…”

Power boundedness in Fourier and Fourier–Stieltjes algebras and other commutative Banach algebras

“…Forrest [9] verified that the analogous description is valid for arbitrary locally compact groups G.…”

Jordan Structures in Harmonic Functions and Fourier Algebras on Homogeneous Spaces

“…It suffices to show that there exists σ U ∈ S(H\G) with supp σ U ⊂ HU which gives the required net (σ U ) U∈U . The existence follows directly from an argument in the proof of Proposition 2.2 in [15].…”