an:05702412 Zbl 1197.46028 Garc\'\i a Armas, Mario; S\'anchez Fern\'andez, Carlos On the solubility of transcendental equations in commutative C*-algebras. EN Banach J. Math. Anal. 4, No. 2, 45-52, electronic only (2010). ISSN 1735-8787/e 2010

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*46J10 46T25 46-01 Banach algebras of continuous functions; transcendental equations; entire functions Summary: 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.