A Course on Topological Vector Spaces

Jürgen Voigt

ISBN 10: 3030329445 / ISBN 13: 9783030329440

Verlag: Springer International Publishing, Springer International Publishing Mär 2020, 2020

Beschreibung

Neuware -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(¿) 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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 164 pp. Englisch.

Bestandsnummer des Verkäufers 9783030329440

Bibliografische Details

• Titel: A Course on Topological Vector Spaces
• Verlag: Springer International Publishing, Springer International Publishing Mär 2020
• Erscheinungsjahr: 2020
• Sprache: Englisch
• ISBN-10: 3030329445
• ISBN-13: 9783030329440
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 235B x 155 H x 10 T Millimeter Breite: 235 mm, Höhe: 155 mm, Tiefe: 10 mm
• Gewicht: 260 Gramm

Über diesen Titel

Inhaltsangabe

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. 

 

Über die Autorin bzw. den Autor

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