Locally Convex Spaces

Abstract

A topological vector space is a generalization of the concept of a Banach space. The locally convex spaces are encountered repeatedly when discussing weak topologies on a Banach space, sets of operators on Hilbert space, or the theory of distributions. This book will only skim the surface of this theory, but it will treat locally convex spaces in sufficient detail as to enable the reader to understand the use of these spaces in the three areas of analysis just mentioned. For more details on this theory, see Bourbaki [1967], Robertson and Robertson [1966], or Schaefer [1971].