Strong Ditkin algebras without bounded relative units

In a previous note the author gave an example of a strong Ditkin algebra which does not have bounded relative units in the sense of Dales. In this note we investigate a certain family of Banach function algebras on the one point compactification of the natural numbers, and see that within this family are many easier examples of strong Ditkin algebras without bounded relative units in the sense of Dales.Comment: 7 pages, plain tex, some extra comments and reference

Endomorphisms of Banach algebras of infinitely differentiable functions on compact plane sets

In this note we study the endomorphisms of certain Banach algebras of infinitely differentiable functions on compact plane sets, associated with weight sequences M. These algebras were originally studied by Dales, Davie and McClure. In a previous paper this problem was solved in the case of the unit interval for many weights M. Here we investigate the extent to which the methods used previously apply to general compact plane sets, and introduce some new methods. In particular, we obtain many results for the case of the closed unit disc. This research was supported by EPSRC grant GR/M31132Comment: 15 pages LaTe

Weak Sequential Completeness of Uniform Algebras

We prove that a uniform algebra is weakly sequentially complete if and only if it is finite-dimensional