Banach Journal of Mathematical Analysis

On the solubility of transcendental equations in commutative C*-algebras

Mario Garcia Armas and Carlos Sanchez Fernandez

Full-text: Open access

Abstract

It is known that $C(X)$ is algebraically closed if $X$ is a locally connected, hereditarily unicoherent compact Hausdorff space. For such spaces, we prove that if $F:C(X) \to C(X)$ is an entire function in the sense of Lorch, i.e., is given by an everywhere convergent power series with coefficients in $C(X)$, and satisfies certain restrictions, then it has a root in $C(X)$. Our results generalizes the monic algebraic case.

Article information

Source
Banach J. Math. Anal., Volume 4, Number 2 (2010), 45-52.

Dates
First available in Project Euclid: 7 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1297117240

Digital Object Identifier
doi:10.15352/bjma/1297117240

Mathematical Reviews number (MathSciNet)
MR2606481

Zentralblatt MATH identifier
1197.46028

Subjects
Primary: 46J10: Banach algebras of continuous functions, function algebras [See also 46E25]
Secondary: 46T25: Holomorphic maps [See also 46G20]

Keywords
Banach algebras of continuous functions transcendental equations entire functions

Citation

Garcia Armas, Mario; Sanchez Fernandez, Carlos. On the solubility of transcendental equations in commutative C*-algebras. Banach J. Math. Anal. 4 (2010), no. 2, 45--52. doi:10.15352/bjma/1297117240. https://projecteuclid.org/euclid.bjma/1297117240


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References

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