A Course on Topological Vector Spaces (Compact Textbooks in Mathematics) - Softcover

Voigt, Jürgen

Softcover

ISBN 10: 3030329445 ISBN 13: 9783030329440

Publisher: Birkhäuser, 2020

Synopsis

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. 

 

About this title

About the Author

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

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. 

Edition details

• Publisher: Birkhäuser
• Publication date: 2020
• Language: English
• ISBN 10: 3030329445
• ISBN 13: 9783030329440
• Binding: Paperback
• Edition number: 1
• Number of pages: 163