A Course on Topological Vector Spaces. 1st ed. 2020

種類:

電子ブック

責任表示:

by Jürgen Voigt

出版情報:

Cham : Springer International Publishing : Imprint: Birkhäuser, 2020

著者名:

• Voigt, Jürgen.
• SpringerLink (Online service)

シリーズ名:

Compact Textbooks in Mathematics ;

ISBN:

9783030329457 [3030329453]    

注記:

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

ローカル注記:

学内専用E-BOOKS (local access only)