| Description |
1 online resource (152 pages) |
| Series |
Compact Textbooks in Mathematics |
|
Compact textbooks in mathematics.
|
| Contents |
Initial topology, topological vector spaces, weak topology.- Convexity, separation theorems, locally convex spaces.- Polars, bipolar theorem, polar topologies.- The theorems of Tikhonov and Alaoglu-Bourbaki.- The theorem of Mackey-Arens.- Topologies on E'', quasi-barrelled and barrelled spaces.- Reflexivity.- Completeness.- Locally convex final topology, topology of D(\Omega).- Precompact -- compact -- complete.- The theorems of Banach -- Dieudonne and Krein-Smulian.- The theorems of Eberlein -- Grothendieck and Eberlein-Smulian.- The theorem of Krein.- Weakly compact sets in L-1(\mu).- \cB-0''=\cB.- The theorem of Krein-Milman.- A The theorem of Hahn-Banach.- B Baire's theorem and the uniform boundedness theorem |
| Summary |
This book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach's theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein's theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(omega) and the space of distributions, and the Krein-Milman theorem |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Print version record |
| Subject |
Vector spaces.
|
|
Espacios vectoriales
|
|
Vector spaces
|
| Form |
Electronic book
|
| ISBN |
9783030329457 |
|
3030329453 |
|
