A Course on Topological Vector Spaces

di Jürgen Voigt (Autore)

Springer Nature Switzerland AG, 2020

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.   

• Autore: Jürgen Voigt
• Editore: Springer Nature Switzerland AG
• Collana: Compact Textbooks in Mathematics
• Anno: 2020
• Rilegatura: Paperback / softback
• Pagine: 155 p.
• Dimensioni: 235 x 155 mm
• EAN: 9783030329440

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