A Course on Topological Vector Spaces

Jürgen Voigt

ISBN 10: 3030329445 / ISBN 13: 9783030329440

Editore: Springer International Publishing, Springer International Publishing, 2020

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Druck auf Anfrage Neuware - Printed after ordering - 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 functionsD( ) 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.

Codice articolo 9783030329440

Dati bibliografici

• Titolo: A Course on Topological Vector Spaces
• Editore: Springer International Publishing, Springer International Publishing
• Data di pubblicazione: 2020
• Lingua: Inglese
• ISBN 10: 3030329445
• ISBN 13: 9783030329440
• Rilegatura: Taschenbuch
• Condizione: Neu

Descrizione articolo

Riassunto

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. 

 

Informazioni sull?autore

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