國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁

切換: 標籤 | MARC模式 | ISBD

A course on topological vector spaces

SpringerLink (Online service)

A course on topological vector spaces

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	A course on topological vector spacesby Jurgen Voigt.
作者:	Voigt, Jurgen.
出版者:	Cham :Springer International Publishing :2020.
面頁冊數:	viii, 155 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
標題:	Vector spaces.
電子資源:	https://doi.org/10.1007/978-3-030-32945-7
ISBN:	9783030329457$q(electronic bk.)

A course on topological vector spaces
Voigt, Jurgen.

A course on topological vector spaces[electronic resource] /by Jurgen Voigt. - Cham :Springer International Publishing :2020. - viii, 155 p. :ill., digital ;24 cm. - Compact textbooks in mathematics,2296-4568. - Compact textbooks in mathematics..

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.

ISBN: 9783030329457$q(electronic bk.)

Standard No.: 10.1007/978-3-030-32945-7doiSubjects--Topical Terms:

210526
Vector spaces.

LC Class. No.: QA186 / .V654 2020

Dewey Class. No.: 515.73

A course on topological vector spaces
LDR:02840nmm a2200337 a 4500 001 572788
003 DE-He213
005 20200806115914.0
006 m d
007 cr nn 008maaau
008 200925s2020 sz s 0 eng d
020 $a 9783030329457$q(electronic bk.)
020 $a 9783030329440$q(paper)
024 7 $a 10.1007/978-3-030-32945-7 $2 doi
035 $a 978-3-030-32945-7
040 $a GP $c GP
041 0 $a eng
050 4 $a QA186 $b .V654 2020
072 7 $a PBKF $2 bicssc
072 7 $a MAT037000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 515.73 $2 23
090 $a QA186 $b .V891 2020
100 1 $a Voigt, Jurgen. $3 860005
245 1 2 $a A course on topological vector spaces $h [electronic resource] / $c by Jurgen Voigt.
260 $a Cham : $b Springer International Publishing : $b Imprint: Birkhauser, $c 2020.
300 $a viii, 155 p. : $b ill., digital ; $c 24 cm.
490 1 $a Compact textbooks in mathematics, $x 2296-4568
505 0 $a 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.
520 $a 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.
650 0 $a Vector spaces. $3 210526
650 1 4 $a Functional Analysis. $3 274845
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
830 0 $a Compact textbooks in mathematics. $3 700241
856 4 0 $u https://doi.org/10.1007/978-3-030-32945-7
950 $a Mathematics and Statistics (Springer-11649)