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

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

2009-11-23

arxiv.org/abs/0911.4469v2

Banach J. Math. Anal. 4 (2010) 45 - 52

Mathematics

Functional Analysis

8 pages

Scientific paper

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 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.

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