Name: A Course on Topological Vector Spaces
Price: 32.95 CAD
Availability: click-8910566-13710609?url=https%3A%2F%2Fwww.chapters.indigo.ca%2Fen-ca%2Fbooks%2Fproduct%2F9783030329440-item.html
Author: Jürgen Voigt
ISBN: 9783030329457

A Course on Topological Vector Spaces

by Jürgen Voigt 2020-05-07 08:11:45

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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 L 1-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. Less

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