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.
| Autorius: | Jürgen Voigt |
| Serija: | Compact Textbooks in Mathematics |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2020 |
| Knygos puslapių skaičius: | 164 |
| ISBN-10: | 3030329445 |
| ISBN-13: | 9783030329440 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Functional analysis and transforms |
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