03456nam 22004935 450 991048362010332120231115135445.03-030-32945-310.1007/978-3-030-32945-7(CKB)5300000000003387(DE-He213)978-3-030-32945-7(MiAaPQ)EBC6132430(PPN)243227035(EXLCZ)99530000000000338720200306d2020 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierA Course on Topological Vector Spaces /by Jürgen Voigt1st ed. 2020.Cham :Springer International Publishing :Imprint: Birkhäuser,2020.1 online resource (VIII, 155 p. 1 illus. in color.)Compact Textbooks in Mathematics,2296-45683-030-32944-5 Includes bibliographical references and indexes.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.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. .Compact Textbooks in Mathematics,2296-4568Functional analysisFunctional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Functional analysis.Functional Analysis.515.73515.73Voigt Jürgenauthttp://id.loc.gov/vocabulary/relators/aut971623MiAaPQMiAaPQMiAaPQBOOK9910483620103321Course on Topological Vector Spaces2983606UNINA