Convergence Structures and Applications to Functional Analysis

✍ Scribed by R. Beattie, H.-P. Butzmann (auth.)

• Publisher: Springer Netherlands
• Year: 2002
• Tongue: English
• Leaves: 271
• Edition: 1
• Category: Library

✦ Synopsis

This text offers a rigorous introduction into the theory and methods of convergence spaces and gives concrete applications to the problems of functional analysis. While there are a few books dealing with convergence spaces and a great many on functional analysis, there are none with this particular focus.

The book demonstrates the applicability of convergence structures to functional analysis. Highlighted here is the role of continuous convergence, a convergence structure particularly appropriate to function spaces. It is shown to provide an excellent dual structure for both topological groups and topological vector spaces.

Readers will find the text rich in examples. Of interest, as well, are the many filter and ultrafilter proofs which often provide a fresh perspective on a well-known result.

Audience: This text will be of interest to researchers in functional analysis, analysis and topology as well as anyone already working with convergence spaces. It is appropriate for senior undergraduate or graduate level students with some background in analysis and topology.

✦ Table of Contents

Front Matter....Pages i-xiii
Convergence spaces....Pages 1-58
Uniform convergence spaces....Pages 59-78
Convergence vector spaces....Pages 79-117
Duality....Pages 119-152
Hahn-Banach extension theorems....Pages 153-181
The closed graph theorem....Pages 183-193
The Banach-Steinhaus theorem....Pages 195-206
Duality theory for convergence groups....Pages 207-246
Back Matter....Pages 247-264

✦ Subjects

Functional Analysis; Topology; Topological Groups, Lie Groups; Real Functions