Endomorphisms of Banach Algebras of Infinitely Differentiable Functions on Compact Plane Sets
✍ Scribed by Joel F. Feinstein; Herbert Kamowitz
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 134 KB
- Volume
- 173
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
Let X be a perfect, compact subset of the complex plane, let (M n ) be a sequence of positive numbers satisfying M 0 =1 and ( m+n n ) M m+n ÂM m M n , and let D(X, M)
With pointwise addition and multiplication, D(X, M) is a commutative normed algebra. In this note we study the endomorphisms of such algebras. In a previous paper this problem was solved when X=[0, 1] for many weights (M n ). Here we investigate the extent to which the methods used previously apply to general X and introduce some new methods. In particular, we obtain many results when X=2 where 2 is the open unit disc.
2000 Academic Press
This note is a sequel to [5] where we investigated the endomorphisms of a certain class of Banach algebras of infinitely differentiable functions on the unit interval.