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APPROXIMATE AMENABILITY OF SEGAL ALGEBRAS
- Part of
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- Journal:
- Journal of the Australian Mathematical Society / Volume 95 / Issue 1 / August 2013
- Published online by Cambridge University Press:
- 18 July 2013, pp. 20-35
- Print publication:
- August 2013
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- Article
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In this paper we first show that for a locally compact amenable group
$G$, every proper abstract Segal algebra of the Fourier algebra on 
$G$ is not approximately amenable; consequently, every proper Segal algebra on a locally compact abelian group is not approximately amenable. Then using the hypergroup generated by the dual of a compact group, it is shown that all proper Segal algebras of a class of compact groups including the 
$2\times 2$ special unitary group, 
$\mathrm{SU} (2)$, are not approximately amenable.
