Completeness of a space of germs of holomorphic functions
Let \(K\) be a balanced compact set in a Fréchet space \(E\) and \(X\) be a Banach space. The space of \(X-\)valued holomorphic functions on \( K\) equipped with the inductive limit topology is denoted by \(H(K,X)\). \textit{S. Dineen} [Lect. Notes Math. 843, 247-263 (1981; Zbl 0474.46011)] has proved that \(H(K)= H(K, {\mathbb C})\) is complete. In this short communication, the author generalizes this result to the vector-valued cases. In fact he shows that \(H(K , X)\) is a complete space.
space of \(X\)-valued holomorphic functions
scientific article; zbMATH DE number 1321725