Foreword

Abstract

This book is designed to present a unified view of the topics in both finite and infinite dimensions. Problems arising from the study of holomorphic continuation and holomorphic approximation have been central in the development of complex analysis in finitely many variables, and constitute one of the most promising lines of current research in infinite dimensional complex analysis. The contents of this book fall naturally into four parts. It presents the basic properties of holomorphic mappings and domains of holomorphy in Banach spaces. Polynomially convex compact sets are investigated in detail, and some of the results obtained are applied to the study of Banach and Frechet algebras. It is devoted to the study of plurisubharmonic functions and pseudoconvex domains in Banach spaces. The identity of pseudoconvex domains and domains of holomorphy is established in the case of separable Banach spaces with the bounded approximation property.