Okada, Susumu, and Ricker, Werner J.. "Criteria for weak compactness of vector-valued integration maps." Commentationes Mathematicae Universitatis Carolinae 35.3 (1994): 485-495. <http://eudml.org/doc/247612>.
@article{Okada1994,
abstract = {Criteria are given for determining the weak compactness, or otherwise, of the integration map associated with a vector measure. For instance, the space of integrable functions of a weakly compact integration map is necessarily normable for the mean convergence topology. Results are presented which relate weak compactness of the integration map with the property of being a bicontinuous isomorphism onto its range. Finally, a detailed description is given of the compactness properties for the integration maps of a class of measures taking their values in $\ell ^1$, equipped with various weak topologies.},
author = {Okada, Susumu, Ricker, Werner J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {weakly compact integration map; factorization of a vector measure; weakly compact integration map; factorization of a vector measure; weak compactness; integration map associated with a vector measure; space of integrable functions of a weakly compact integration map; mean convergence topology; bicontinuous isomorphism},
language = {eng},
number = {3},
pages = {485-495},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Criteria for weak compactness of vector-valued integration maps},
url = {http://eudml.org/doc/247612},
volume = {35},
year = {1994},
}
TY - JOUR
AU - Okada, Susumu
AU - Ricker, Werner J.
TI - Criteria for weak compactness of vector-valued integration maps
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 3
SP - 485
EP - 495
AB - Criteria are given for determining the weak compactness, or otherwise, of the integration map associated with a vector measure. For instance, the space of integrable functions of a weakly compact integration map is necessarily normable for the mean convergence topology. Results are presented which relate weak compactness of the integration map with the property of being a bicontinuous isomorphism onto its range. Finally, a detailed description is given of the compactness properties for the integration maps of a class of measures taking their values in $\ell ^1$, equipped with various weak topologies.
LA - eng
KW - weakly compact integration map; factorization of a vector measure; weakly compact integration map; factorization of a vector measure; weak compactness; integration map associated with a vector measure; space of integrable functions of a weakly compact integration map; mean convergence topology; bicontinuous isomorphism
UR - http://eudml.org/doc/247612
ER -