A Course on Topological Vector Spaces / Compact Textbooks in Mathematics (PDF)
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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(O) 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.
- Autor: Jürgen Voigt
- 2020, 1st ed. 2020, 155 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3030329453
- ISBN-13: 9783030329457
- Erscheinungsdatum: 06.03.2020
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- Dateiformat: PDF
- Größe: 1.92 MB
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