Convergence Structures and Applications to Functional Analysis

by R. Beattie, Heinz-Peter Butzmann

Overview

Convergence vector spaces and the application of continuous convergence overcome many problems inherent in other forms of functional analysis, argue Beattie (mathematics and computer science, Mount Allison U., Canada) and Butzmann (mathematics and information science, U. Mannheim, Germany). After introducing the basic theory of convergence spaces and convergence vector spaces, they describe a number of functional analytic applications, specifically related to continuous convergence as a duality structure, the Hahn-Banach extension theorem, the closed graph theorem, the Banach- Steinhaus theorem, and duality and reflexivity for convergence groups. Annotation (c)2003 Book News, Inc., Portland, OR

Product Details

ISBN-13:	9781402005664
Publisher:	Springer Netherlands
Publication date:	03/31/2002
Edition description:	2002
Pages:	264
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

1 Convergence spaces.- 2 Uniform convergence spaces.- 3 Convergence vector spaces.- 4 Duality.- 5 Hahn-Banach extension theorems.- 6 The closed graph theorem.- 7 The Banach-Steinhaus theorem.- 8 Duality theory for convergence groups.- List of Notations.