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The book delves into the theory of topological vector spaces, emphasizing locally convex spaces. It explores topologies in dual pairs and presents significant results such as the Mackey-Arens theorem. Key properties of weak topology on Banach spaces are examined, including Banach's theorem regarding weak*-closed subspaces, the Eberlein-Smulian theorem, Krein's insights on weakly compact sets, and the Dunford-Pettis theorem that defines weak compactness. This comprehensive approach offers valuable insights for advanced studies in functional analysis.
Nákup knihy
A Course on Topological Vector Spaces, Jürgen Voigt
- Jazyk
- Rok vydania
- 2020
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- Titul
- A Course on Topological Vector Spaces
- Jazyk
- anglicky
- Autori
- Jürgen Voigt
- Vydavateľ
- Springer International Publishing
- Rok vydania
- 2020
- Väzba
- mäkká
- Počet strán
- 164
- ISBN13
- 9783030329440
- Kategórie
- Matematika
- Anotácia
- The book delves into the theory of topological vector spaces, emphasizing locally convex spaces. It explores topologies in dual pairs and presents significant results such as the Mackey-Arens theorem. Key properties of weak topology on Banach spaces are examined, including Banach's theorem regarding weak*-closed subspaces, the Eberlein-Smulian theorem, Krein's insights on weakly compact sets, and the Dunford-Pettis theorem that defines weak compactness. This comprehensive approach offers valuable insights for advanced studies in functional analysis.