H. G. Dales

The second duals of Beurling algebras

Introduction Definitions and preliminary results Repeated limit conditions Examples Introverted subspaces Banach algebras of operators Beurling algebras The second dual of

The Amenability of Measure Algebras

\ell^1(G,\omega)

THE SECOND TRANSPOSE OF A DERIVATION

Algebras on discrete, Abelian groups Beurling algebras on

Quasianalytic Banach function algebras

\mathbb{F}_2

Stability of mappings on multi-normed spaces

Topological centres of duals of introverted subspaces The second dual of

Algebraic and strong splittings of extensions of Banach algebras

L^1(G,\omega)

Norms and ideals in radical convolution algebras

Derivations into second duals Open questions Bibliography Index Index of symbols.

Homological properties of modules over group algebras

In this paper we shall prove that the measure algebra M(G) of a locally compact group G is amenable as a Banach algebra if and only if G is discrete and amenable as a group. Our contribution is to resolve a conjecture by proving that M(G) is not amenable in the case where the group G is not discrete. Indeed, we shall prove a much stronger result: the measure algebra of a non-discrete, locally compact group has a non-zero, continuous point derivation at a certain character on the algebra.

The Wedderburn decomposability of some commutative Banach algebras

Let A be a Banach algebra, and let D: A → A* be a continuous derivation, where A* is the topological dual space of A. The paper discusses the situation when the second transpose D**: A** → (A**)* is also a derivation in the case where A** has the first Arens product.

Continuity of Derivations, Intertwining Maps, and Cocycles from Banach Algebras

We construct certain Banach algebras of infinitely differentiable functions on compact plane sets such that the algebras are quasianalytic, and we use these algebras to construct examples of Banach algebras defined on their maximal ideal spaces which, first, have only countably many peak points and, second, have the property that a discontinuous function operates on the algebra. We show that any function defined on an open subset of the plane which operates on a Banach function algebra is necessarily continuous on a dense open subset of its domain.