A course on topological vector spaces

• 作者： Voigt, Jurgen, author.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Compact textbooks in mathematics.
• 出版： Cham : Springer International Publishing :Imprint: Birkhauser
• 叢書名： Compact textbooks in mathematics,
• 主題： Vector spaces. , Functional Analysis.
• ISBN： 9783030329457 (electronic bk.) 、 9783030329440 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: Initial topology, topological vector spaces, weak topology -- Convexity, separation theorems, locally convex spaces -- Polars, bipolar theorem, polar topologies -- The theorems of Tikhonov and Alaoglu-Bourbaki -- The theorem of Mackey-Arens -- Topologies on E'', quasi-barrelled and barrelled spaces -- Reflexivity -- Completeness -- Locally convex final topology, topology of D(Omega) -- Precompact -- compact - complete -- The theorems of Banach--Dieudonne and Krein-Smulian -- The theorems of Eberlein--Grothendieck and Eberlein-Smulian -- The theorem of Krein -- Weakly compact sets in L_1(mu) -- cB_0''=cB -- The theorem of Krein-Milman -- A The theorem of Hahn-Banach -- B Baire's theorem and the uniform boundedness theorem.
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• 摘要註: 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(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.
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