• ISBN13: 9783030329440
• Binding: Paperback
• Subject: Mathematics and Statistics
• Publisher: Springer Verlag
• Publisher Imprint: Birkhäuser
• Publication Date: January 1, 2020
• Pages: 155
• Original Price: EUR 37.99
• Language: English
• Edition: N/A
• Item Weight: 241 grams
• BISAC Subject(s): Functional Analysis and Calculus

From the Back Cover

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.

Jürgen Voigt is Professor at the Institute of Analysis of the Technische Universität in Dresden, Germany.