A Course on Topological Vector Spaces (Paperback, 1st ed. 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( ) 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.

General

Imprint:	Springer Nature Switzerland AG
Country of origin:	Switzerland
Series:	Compact Textbooks in Mathematics
Release date:	March 2020
First published:	2020
Authors:	Jurgen Voigt
Dimensions:	235 x 155mm (L x W)
Format:	Paperback
Pages:	155
Edition:	1st ed. 2020
ISBN-13:	978-3-03-032944-0
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Functional analysis
LSN:	3-03-032944-5
Barcode:	9783030329440

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