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A course on topological vector spaces

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A course on topological vector spaces

Record Type:	Electronic resources : Monograph/item
Title/Author:	A course on topological vector spacesby Jurgen Voigt.
Author:	Voigt, Jurgen.
Published:	Cham :Springer International Publishing :2020.
Description:	viii, 155 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Vector spaces.
Online resource:	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
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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.
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