Convergence structures and applications to functional analysis / by R. Beattie and H.-P. Butzmann.

Format:

Book

Author/Creator:

Beattie, R.

Contributor:

Butzmann, H.-P.

Anne and Joseph Trachtman Memorial Book Fund.

Language:

English

Subjects (All):

Functional analysis.

Convergence.

Physical Description:

xiii, 264 pages ; 25 cm

Place of Publication:

Dordrecht ; Boston : Kluwer Academic Publishers, [2002]

Contents:

1 Convergence spaces 1

1.2 Initial and final convergence structures 4

1.3 Special convergence spaces, modifications 10

1.4 Compactness 21

1.5 The continuous convergence structure 25

1.6 Countability properties and sequences in convergence spaces 42

1.7 Sequential convergence structures 51

1.8 Categorical aspects 57

2 Uniform convergence spaces 59

2.1 Generalities on uniform convergence spaces 59

2.2 Initial and final uniform convergence structures 67

2.3 Complete uniform convergence spaces 69

2.4 The Arzela-Ascoli theorem 71

2.5 The uniform convergence structure of a convergence group 75

3 Convergence vector spaces 79

3.1 Convergence groups 79

3.2 Generalities on convergence vector spaces 85

3.3 Initial and final vector space convergence structures 88

3.4 Projective and inductive limits of convergence vector spaces 96

3.5 The locally convex topological modification 102

3.6 Countability axioms for convergence vector spaces 109

3.7 Boundedness 111

3.8 Notes on bornological vector spaces 116

4 Duality 119

4.1 The dual of a convergence vector space 119

4.2 Reflexivity 125

4.3 The dual of a locally convex topological vector space 131

4.4 An application of continuous duality 148

5 Hahn-Banach extension theorems 153

5.1 General results 154

5.2 Hahn-Banach spaces 160

5.3 Extending to the adherence 164

5.4 Strong Hahn-Banach spaces 172

5.5 An application to partial differential equations 178

6 The closed graph theorem 183

6.1 Ultracompleteness 184

6.2 The main theorems 187

6.3 An application to web spaces 192

7 The Banach-Steinhaus theorem 195

7.1 Equicontinuous sets 196

7.2 Banach-Steinhaus pairs 198

7.3 The continuity of bilinear mappings 204

8 Duality theory for convergence groups 207

8.1 Reflexivity 208

8.2 Duality for convergence vector spaces 215

8.3 Subgroups and quotient groups 217

8.4 Topological groups 224

8.5 Groups of unimodular continuous functions 232

8.6 c- and co-duality for topological groups 240.

Notes:

Includes bibliographical references (pages 247-256) and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

1402005660

OCLC:

49552048