A Simple Proof of the Borel Extension Theorem and Weak Compactness of Operators
Authors: Dobrakov I.1; Panchapagesan T.V.2
Source: Czechoslovak Mathematical Journal, Volume 52, Number 4, December 2002 , pp. 691-703(13)
Publisher: Springer
- Free Content
- New Content
- Subscribed Content
- Free Trial Content
Abstract:
Let T be a locally compact Hausdorff space and let C0(T) be the Banach space of all complex valued continuous functions vanishing at infinity in T, provided with the supremum norm. Let X be a quasicomplete locally convex Hausdorff space. A simple proof of the theorem on regular Borel extension of X-valued
-additive Baire measures on T is given, which is more natural and direct than the existing ones. Using this result the integral representation and weak compactness of a continuous linear map u: C0(T) 
X when C0 
X are obtained. The proof of the latter result is independent of the use of powerful results such as Theorem 6 of [6] or Theorem 3 (vii) of [13].
Keywords:
weakly compact operator on C0(T);
representing measure;
lcHs-valued -additive Baire (or regular Borel, or regular -Borel) measures
Document Type: Research article
DOI: 10.1023/B:CMAJ.0000027224.01146.63
Affiliations:
1:
Mathematical Institute, Slovak Academy of Sciences, 
tefánikova 49, Bratislava, Slovakia
tefánikova 49, Bratislava, Slovakia
">
2:
Departamento de matemáticas, Facultad de Ciencias, Universidad de los Andes, Merida, Venezuela, Email: panchapa@ciens.ula.ve
- Free Content
- New Content
- Subscribed Content
- Free Trial Content
Click here for Page Help