A Course on Topological Vector Spaces 2020 Edition Contributor(s): Voigt, Jürgen (Author) |
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ISBN: 3030329445 ISBN-13: 9783030329440 Publisher: Birkhauser OUR PRICE: $42.74 Product Type: Paperback Published: March 2020 |
Additional Information |
BISAC Categories: - Mathematics | Functional Analysis - Mathematics | Calculus |
Dewey: 515.7 |
Series: Compact Textbooks in Mathematics |
Physical Information: 0.35" H x 6.14" W x 9.21" (0.53 lbs) 155 pages |
Descriptions, Reviews, Etc. |
Publisher Description: 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.
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