A Course on Topological Vector Spaces - 9783030329440

A Course on Topological Vector SpacesAuthor(s): Jrgen Voigt\nFormat: Paperback\nPublisher: Springer Nature Switzerland AG, Switzerland\nImprint: Springer Nature Switzerland AG\nISBN-13: 9783030329440, 978-3030329440\nSynopsis\nThis 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 functionsD(?) and the space of distributions, and the Krein-Milman theorem.\n\nThe book ado.