2,789 research outputs found
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
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