Completeness of a space of germs of holomorphic functions
type: Item
instance of: scholarly article
title: Completeness of a space of germs of holomorphic functions
zbMATH Open document ID: 0935.46035
author: Nguyen Van Hao
published in: Vietnam Journal of Mathematics
publication date: 1999-11-03T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 46E50
zbMATH DE Number: 1321725
zbMATH Keywords: Fréchet space
zbMATH Keywords: space of \(X\)-valued holomorphic functions
zbMATH Keywords: inductive limit topology
reviewed by: Jafar Zafarani
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1321725