Spectra of algebras of holomorphic functions on infinite dimensional Riemann domains (Q1075555)

Let X be a connected Riemann domain over a separable Fréchet space with the bounded approximation property. Let H(X) be the algebra of all holomorphic functions on X, with the compact-open topology. In this paper it is shown that the set of all bounded complex holomorphisms of H(X) can be canonically identified with the envelope of holomorphy of X, and in particular each bounded complex homomorphism of H(X) is continuous. This result answers a question raised by \textit{M. Schottenloher} [Math. Ann. 263, 213-219 (1983; Zbl 0515.32005)], and is obtained with the aid of the machinery developed by the author in [Stud. Math. 82, 107-134 (1985; Zbl 0584.32035)].