Beschreibung
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 Banachs theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Kreins 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.
Herstellerkennzeichnung:
Springer Basel AG in Springer Science + Business Media
Heidelberger Platz 3
14197 Berlin
DE
E-Mail: juergen.hartmann@springer.com
![Produktbild: Generalized Closed Fuzzy Sets in [0,1]-topological Spaces](http://medien.umbreitkatalog.de/bildzentrale/978/365/911/9545.jpg)
