EAN: 9783030329440

Bilder-Quelle: discount24.de - Sport-Freizeit

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.

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