J. Aust. Math. Soc.
80 (2006), 317333

Relative amenability and the nonamenability of


Abstract

In this paper we begin with a short, direct
proof that the Banach algebra
is not amenable. We continue by showing that
various direct sums of matrix algebras are not
amenable either, for example the direct sum of
the finite dimensional algebras
is not amenable for
,
. Our method of proof naturally involves free
group algebras, (by which we mean certain
subalgebras of
for some space with symmetric basis—not necessarily
) and we introduce the notion of 'relative
amenability' of these algebras.

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