| 期刊全稱 | A Course on Topological Vector Spaces | | 影響因子2023 | Jürgen Voigt | | 視頻video | http://file.papertrans.cn/141/140533/140533.mp4 | | 發(fā)行地址 | Includes a streamlined introduction to the duality theory of locally convex spaces, culminating in the Mackey-Arens theorem.Treats various important topics concerning the weak topology of Banach space | | 學科分類 | Compact Textbooks in Mathematics | | 圖書封面 |  | | 影響因子 | .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. L.1.-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions?D(Ω) 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.?..?. | | Pindex | Textbook 2020 |
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