bokomslag A Course on Topological Vector Spaces
Vetenskap & teknik

A Course on Topological Vector Spaces

Jrgen Voigt

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  • 155 sidor
  • 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 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.
  • Författare: Jrgen Voigt
  • Format: Pocket/Paperback
  • ISBN: 9783030329440
  • Språk: Engelska
  • Antal sidor: 155
  • Utgivningsdatum: 2020-03-07
  • Förlag: Springer Nature Switzerland AG