an: Zbl 1197.46028
au: Garc\'\i a Armas, Mario; S\'anchez Fern\'andez, Carlos
ti: On the solubility of transcendental equations in commutative C*-algebras.
la: EN
so: Banach J. Math. Anal. 4, No. 2, 45-52, electronic only (2010).
py: 2010
dt: J
cc: *46J10 46T25 46-01
ut: Banach algebras of continuous functions; transcendental equations; entire
    functions
ab: 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.