Amenability and the second dual of a Banach algebra
Amenability and the Arens product are studied. Using the Arens product, derivations from A are extended to derivations from A**. This is used to show directly that A** amenable implies A amenable.
Homology and cohomology of Rees semigroup algebras
Let S be a Rees semigroup, and let ℓ¹(S) be its convolution semigroup algebra. Using Morita equivalence we show that bounded Hochschild homology and cohomology of ℓ¹(S) are isomorphic to those of the underlying discrete group algebra.
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