A simple proof of the Borel extension theorem and weak compactness of operators

Dobrakov, Ivan, and Panchapagesan, Thiruvaiyaru V.. "A simple proof of the Borel extension theorem and weak compactness of operators." Czechoslovak Mathematical Journal 52.4 (2002): 691-703. <http://eudml.org/doc/30735>.

@article{Dobrakov2002,
abstract = {Let $T$ be a locally compact Hausdorff space and let $C_0(T)$ 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 $\sigma $-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 $u\: C_0(T) \rightarrow X$ when $c_0 \lnot \subset X$ 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].},
author = {Dobrakov, Ivan, Panchapagesan, Thiruvaiyaru V.},
journal = {Czechoslovak Mathematical Journal},
keywords = {weakly compact operator on $C_0(T)$; representing measure; lcHs-valued $\sigma $-additive Baire (or regular Borel; or regular $\sigma $-Borel) measures; weakly compact operator on ; representing measure; lcHs-valued -additive Baire measure; regular Borel measure; regular -Borel measure},
language = {eng},
number = {4},
pages = {691-703},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A simple proof of the Borel extension theorem and weak compactness of operators},
url = {http://eudml.org/doc/30735},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Dobrakov, Ivan
AU - Panchapagesan, Thiruvaiyaru V.
TI - A simple proof of the Borel extension theorem and weak compactness of operators
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 4
SP - 691
EP - 703
AB - Let $T$ be a locally compact Hausdorff space and let $C_0(T)$ 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 $\sigma $-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 $u\: C_0(T) \rightarrow X$ when $c_0 \lnot \subset X$ 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].
LA - eng
KW - weakly compact operator on $C_0(T)$; representing measure; lcHs-valued $\sigma $-additive Baire (or regular Borel; or regular $\sigma $-Borel) measures; weakly compact operator on ; representing measure; lcHs-valued -additive Baire measure; regular Borel measure; regular -Borel measure
UR - http://eudml.org/doc/30735
ER -