, Volume 121, Issue 4, pp 353-379

Some results about the spectrum of commutative Banach algebras under the weak topology and applications

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Abstract

LetA be a commutative Banach algebra with a nonempty spectrum ΣA. By “weak” we denote the relative weak topology induced on ΣA by σ(A *,A **). In this note we study some properties of the topological space (ΣA, weak) and present some applications of the results obtained and tools used to amenability, weakly compact homomorphisms, weakly compact subsets of the spectrum of the uniform algebras and to a characterization of the synthesizable ideals of the algebraA.