A Course on Topological Vector Spaces - Couverture souple

Voigt, Jürgen

Couverture souple

ISBN 10 : 3030329445 ISBN 13 : 9783030329440

Editeur : 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. 

 

A propos du livre

À propos de l?auteur

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

Détails de l'édition

• Éditeur: Birkhäuser
• Date d'édition: 2020
• Langue: anglais
• ISBN 10: 3030329445
• ISBN 13: 9783030329440
• Reliure: Broché
• Nombre de pages: 164
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne