Jürgen Voigt: A Course on Topological Vector Spaces
A Course on Topological Vector Spaces
Buch
- Springer International Publishing, 03/2020
- Einband: Kartoniert / Broschiert, Paperback
- Sprache: Englisch
- ISBN-13: 9783030329440
- Bestellnummer: 10054711
- Umfang: 164 Seiten
- Nummer der Auflage: 20001
- Auflage: 1st ed. 2020
- Gewicht: 269 g
- Maße: 233 x 157 mm
- Stärke: 12 mm
- Erscheinungstermin: 7.3.2020
- Serie: Compact Textbooks in Mathematics
Achtung: Artikel ist nicht in deutscher Sprache!
Klappentext
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( ) and the space of distributions, and the Krein-Milman theorem.The book adopts an economic approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians.