LEADER 03456nam  22004935  450 
001 9910483620103321
005 20231115135445.0
010   $a3-030-32945-3
024 7 $a10.1007/978-3-030-32945-7
035   $a(CKB)5300000000003387
035   $a(DE-He213)978-3-030-32945-7
035   $a(MiAaPQ)EBC6132430
035   $a(PPN)243227035
035   $a(EXLCZ)995300000000003387
100   $a20200306d2020      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 12$aA Course on Topological Vector Spaces /$fby Jürgen Voigt
205   $a1st ed. 2020.
210  1$aCham :$cSpringer International Publishing :$cImprint: Birkhäuser,$d2020.
215   $a1 online resource (VIII, 155 p. 1 illus. in color.)
225 1 $aCompact Textbooks in Mathematics,$x2296-4568
311   $a3-030-32944-5 
320   $aIncludes bibliographical references and indexes.
327   $aInitial 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.
330   $aThis book provides an introduction to the theory of topological vector spaces, with a focus on locally convex spaces. It discusses topologies in dual pairs, culminating in the Mackey-Arens theorem, and also examines the properties of the weak topology on Banach spaces, for instance Banach?s theorem on weak*-closed subspaces on the dual of a Banach space (alias the Krein-Smulian theorem), the Eberlein-Smulian theorem, Krein?s theorem on the closed convex hull of weakly compact sets in a Banach space, and the Dunford-Pettis theorem characterising weak compactness in L1-spaces. Lastly, it addresses topics such as the locally convex final topology, with the application to test functions D(?) and the space of distributions, and the Krein-Milman theorem. The book adopts an ?economic? approach to interesting topics, and avoids exploring all the arising side topics. Written in a concise mathematical style, it is intended primarily for advanced graduate students with a background in elementary functional analysis, but is also useful as a reference text for established mathematicians. .
410  0$aCompact Textbooks in Mathematics,$x2296-4568
606   $aFunctional analysis
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
615  0$aFunctional analysis.
615 14$aFunctional Analysis.
676   $a515.73
676   $a515.73
700   $aVoigt$b Jürgen$4aut$4http://id.loc.gov/vocabulary/relators/aut$0971623
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910483620103321
996   $aCourse on Topological Vector Spaces$92983606
997   $aUNINA