Brian E. Forrest

Ideals with bounded approximate identities in Fourier algebras

Abstract We make use of the operator space structure of the Fourier algebra A(G) of an amenable locally compact group to prove that if H is any closed subgroup of G, then the ideal I(H) consisting of all functions in A(G) vanishing on H has a bounded approximate identity. This result allows us to completely characterize the ideals of A(G) with bounded approximate identities. We also show that for several classes of locally compact groups, including all nilpotent groups, I(H) has an approximate identity with norm bounded by 2, the best possible norm bound.

AMENABILITY AND IDEALS IN A(G)

Closed ideals in A(G) with bounded approximate identities are characterized for amenable [SIN]-groups and arbitrary discrete groups. This extends a result of Liu, van Rooij and Wang for abelian groups.

Operator Amenability of the Fourier Algebra in the cb-Multiplier Norm

Let

Projectivity of modules over Fourier algebras

G

Norm one idempotent cb-multipliers with applications to the Fourier algebra in the cb-multiplier norm

be a locally compact group, and let

Best bounds for approximate identities in ideals of the Fourier algebra vanishing on subgroups

A_\cb(G)

Weak amenability and the second dual of the Fourier algebra

denote the closure of

Extending multipliers of the Fourier algebra from a subgroup

A(G)

Uniformly Continuous Functionals and M-Weakly Amenable Groups

, the Fourier algebra of

Leinert sets and complemented ideals in Fourier algebras

G