Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-15T16:50:28.105Z Has data issue: false hasContentIssue false
  • English
  • Français

Semi-algebras in C(T)

Published online by Cambridge University Press:  18 May 2009

Bertram Yood
Bertram Yood
Affiliation:
Pennsylvania State University, University Park, Pa. 16802, U.S.A.
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let C(T) be the Banach algebra of all complex-valued continuous functions on the compact set T of all complex numbers with modulus one. As usual we may suppose that A is embedded in C(T), where A is the disc algebra, i.e., the algebra of all complex-valued functions f(λ) continuous for |λ| ≦ 1. and analytic for |λ| < 1. We set Mλ = {f ∈ A: f(λ) = 0} and Mλ = {f ∈ A: f(λ) ≧ 0}.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 15 , Issue 1 , March 1974 , pp. 85 - 87
Copyright
Copyright © Glasgow Mathematical Journal Trust 1974

References

REFERENCES

1.Bonsall, F. F., Semi-algebras of continuous functions, Proc. London Math. Soc. (3) 10 (1960), 122–140.CrossRefGoogle Scholar
2.Caratheodory, C., Theory of functions of a complex variable, Vol. 2 (Chelsea 1960).Google Scholar
3.Civin, P. and White, C. C., Maximal closed preprimes in Banach algebras, Trans. Amer. Math. Soc. 147 (1970), 241–260.CrossRefGoogle Scholar
4.Harrison, D. K., Finite and infinite primes for rings and fields, Mem. Amer. Math. Soc. No. 68 (1966).Google Scholar
5.Wermer, J., On algebras of continuous functions, Proc. Amer. Math. Soc. 4 (1953), 866–869.CrossRefGoogle Scholar