Event Details

Speaker: Brian Forrest (Waterloo) Title: Bounded approximate identities and amenability of ideals in the Fourier algebra of a locally compact group

Abstract: A Banach algebra A is amenable if every bounded derivation D : A → X* is inner

whenever X is any Banach bimodule of A. If A has an operator space structure that

makes A into a completely contractive Banach algebra, then we say that A is operator

amenable if and only if every completely bounded derivation D : A → X* is inner

whenever X is any operator bimodule of A.

The Fourier algebra A(G) of a locally compact group G is the commutative Banach algebra

of functions on G consisting of coefficient functions of the left regular representation

λ : G → B(L²(G)). It is known that A(G) is amenable if and only if G has an abelian

subgroup of finite index. In contrast, A(G), which carries an distinguished operator space

structure by virtue of being the predual of a von Neumann algebra, is operator amenable

if and only if G is amenable.

In this talk, we will consider closed ideals in A(G) which are (operator) amenable

for a general locally compact group G. In particular, we will show that many even nonamenable

groups have closed (operator) amenable ideals with arbitrarily large amenability

constants.