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Autore: |
Voigt Jürgen
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Titolo: |
A Course on Topological Vector Spaces / / by Jürgen Voigt
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Pubblicazione: | Cham : , : Springer International Publishing : , : Imprint : Birkhäuser, , 2020 |
Edizione: | 1st ed. 2020. |
Descrizione fisica: | 1 online resource (VIII, 155 p. 1 illus. in color.) |
Disciplina: | 515.73 |
Soggetto topico: | Functional analysis |
Functional Analysis | |
Nota di bibliografia: | Includes bibliographical references and indexes. |
Nota di contenuto: | 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. |
Sommario/riassunto: | 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. . |
Titolo autorizzato: | Course on Topological Vector Spaces ![]() |
ISBN: | 3-030-32945-3 |
Formato: | Materiale a stampa ![]() |
Livello bibliografico | Monografia |
Lingua di pubblicazione: | Inglese |
Record Nr.: | 9910483620103321 |
Lo trovi qui: | Univ. Federico II |
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