2020 | Buch
A Course on Topological Vector Spaces
Buchreihe: Compact Textbooks in Mathematics
Autor: Jürgen Voigt
Verlag: Springer International Publishing
Print ISBN: 978-3-030-32944-0
Electronic ISBN: 978-3-030-32945-7
2020 | Buch
Buchreihe: Compact Textbooks in Mathematics
Autor: Jürgen Voigt
Verlag: Springer International Publishing
Print ISBN: 978-3-030-32944-0
Electronic ISBN: 978-3-030-32945-7
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(Ω) 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.
Version: 0.705.0