@article{1197.46028,
author="Garc\'\i a Armas, Mario and S\'anchez Fern\'andez, Carlos",
title="{On the solubility of transcendental equations in commutative
    C*-algebras.}",
language="English",
journal="Banach J. Math. Anal. ",
volume="4",
number="2",
pages="45-52",
year="2010",
abstract="{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.}",
keywords="{Banach algebras of continuous functions; transcendental equations;
    entire functions}",
classmath="{*46J10 (Banach algebras of continuous functions)
46T25 (Holomorphic maps in nonlinear functional analysis)
46-01 (Textbooks (functional analysis))
}",
}