A Borel extension approach to weakly compact operators on C 0 ( T )

Thiruvaiyaru V. Panchapagesan

Czechoslovak Mathematical Journal (2002)

  • Volume: 52, Issue: 1, page 97-115
  • ISSN: 0011-4642

Abstract

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Let X be a quasicomplete locally convex Hausdorff space. Let T be a locally compact Hausdorff space and let C 0 ( T ) = { f T → I , f is continuous and vanishes at infinity } be endowed with the supremum norm. Starting with the Borel extension theorem for X -valued σ -additive Baire measures on T , an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map u C 0 ( T ) → X to be weakly compact.

How to cite

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Panchapagesan, Thiruvaiyaru V.. "A Borel extension approach to weakly compact operators on $C_0(T)$." Czechoslovak Mathematical Journal 52.1 (2002): 97-115. <http://eudml.org/doc/30688>.

@article{Panchapagesan2002,
abstract = {Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_0(T) = \lbrace f\: T \rightarrow I$, $f$ is continuous and vanishes at infinity$\rbrace $ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$-valued $\sigma $-additive Baire measures on $T$, an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map $u\: C_0(T) \rightarrow X$ to be weakly compact.},
author = {Panchapagesan, Thiruvaiyaru V.},
journal = {Czechoslovak Mathematical Journal},
keywords = {convex Hausdorff space; Borel extension theorem; weakly compact operator},
language = {eng},
number = {1},
pages = {97-115},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Borel extension approach to weakly compact operators on $C_0(T)$},
url = {http://eudml.org/doc/30688},
volume = {52},
year = {2002},
}

TY - JOUR
AU - Panchapagesan, Thiruvaiyaru V.
TI - A Borel extension approach to weakly compact operators on $C_0(T)$
JO - Czechoslovak Mathematical Journal
PY - 2002
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 52
IS - 1
SP - 97
EP - 115
AB - Let $X$ be a quasicomplete locally convex Hausdorff space. Let $T$ be a locally compact Hausdorff space and let $C_0(T) = \lbrace f\: T \rightarrow I$, $f$ is continuous and vanishes at infinity$\rbrace $ be endowed with the supremum norm. Starting with the Borel extension theorem for $X$-valued $\sigma $-additive Baire measures on $T$, an alternative proof is given to obtain all the characterizations given in [13] for a continuous linear map $u\: C_0(T) \rightarrow X$ to be weakly compact.
LA - eng
KW - convex Hausdorff space; Borel extension theorem; weakly compact operator
UR - http://eudml.org/doc/30688
ER -

References

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