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

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

1999-05-20

arxiv.org/abs/math/9905135v1

Mathematics

Functional Analysis

15 pages LaTeX

Scientific paper

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/M31132

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