Convergence Structures and Applications to Functional Analysis by R. BeattieConvergence Structures and Applications to Functional Analysis by R. Beattie

Convergence Structures and Applications to Functional Analysis

byR. Beattie, Heinz-Peter Butzmann

Paperback | December 15, 2010

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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.
Title:Convergence Structures and Applications to Functional AnalysisFormat:PaperbackDimensions:277 pagesPublished:December 15, 2010Publisher:Springer NetherlandsLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:9048159946

ISBN - 13:9789048159949

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Table of Contents

Introduction. 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. Bibliography. List of Notations. Index